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1 Introduction1

2 Expository books on mathematics and mathematicians5

2.1 Popular and expository books on mathematics6

2.1.1 R.Courant,H.Robbins,What Is Mathematics? Oxford University Press,New York,1941.xix+521 pp6

2.1.2 A.D.Aleksandrov,A.N.Kolmogorov,M.A.Lavrent'ev,Mathemat-ics:Its Content,Methods,and Meaning.Vol.Ⅰ,Vol.Ⅱ,Vol.Ⅲ,The M.I.T.Press,Cambridge,Mass.,1963,xi+359 pp.;xi+377 pp.;xi+356 pp..Translated by S.H.Gould and T.Bartha;S.H.Gould;K.Hirsch12

2.1.3 G.Pólya,How to Solve it.A New Aspect of Mathematical Method.Expanded version of the 1988 edition,with a new foreword by John H.Conway,Princeton Science Library,Princeton University Press,2004.xxviii+253 pp15

2.1.4 G.H.Hardy,A Mathematician's Apology,With a foreword by C.P.Snow,Reprint of the 1967 edition,Canto,Cambridge University Press,Cambridge,199219

2.1.5 J.E.Littlewood,Littlewood's Miscellany,Edited and with a fore-word by Bola Bollobas,Cambridge University Press,Cambridge,1986.vi+200 pp21

2.1.6 Autobiographies of mathematicians22

2.1.7 H.Weyl,Symmetry.Reprint of the 1952 original.Princeton Sci-ence Library.Princeton University Press,Princeton,N.J.,198927

2.1.8 D.Hilbert,S.Cohn-Vossen,Geometry and the Imagination,Amer-ican Mathematical Society,1,1999.35 7 pages37

2.2 Biographies of mathematicians and history of mathematics42

2.2.1 E.T.Bell,Men of Mathematics,Touchstone,1986.6 08 pages42

2.2.2 C.Reid,Hilbert,Springer-Verlag,New York-Berlin,1970.xi+290 pp44

2.2.3 More biographies of mathematicians46

2.2.4 A.Weil,Number Theory.An Approach through History.From Hammurapi to Legendre.Birkh？user Boston,MA,1984.xxi+375 pp55

2.2.5 W.Scharlau,H.Opolka,From Fermat to Minkowski.Lectures on the Theory of Numbers and its Historical Development,Under-graduate Texts in Mathematics.Springer-Verlag,New York,1985.xi+184 pp58

2.2.6 History of mathematics59

2.2.7 More mathematical history books62

2.2.8 J.Dieudonné,A History of Algebraic and Differential Topology 1900-1960,Reprint of the 1989 edition,Modern Birkh？user Clas-sics.Birkh？user Boston,Inc.,Boston,MA,2009.xxii+648 pp72

2.2.9 History of Lie groups and related spaces73

2.2.10 F.Klein,Development of Mathematics in the 19th Century,With a preface and appendices by Robert Hermann,Translated from the German by M.Ackerman.Math Sci Press,Brookline,Mass.,1979.ix+630 pp75

3 Analysis79

3.1 Calculus and real analysis79

3.1.1 G.H.Hardy,A Course of Pure Mathematics,Reprint of the(1952) tenth edition,Cambridge Mathematical Library,Cambridge Uni-versity Press,Cambridge,1992.xii+509 pp80

3.1.2 Calculus82

3.1.3 E.T.Whittaker and G.N.Watson,A Course of Modern Analysis,An Introduction to the General Theory of Infinite Processes and of Analytic Functions:with an Account of the Principal Transcen-dental Functions,Fourth edition.Reprinted,Cambridge University Press,New York,1962,vii+608 pp85

3.1.4 Special functions85

3.1.5 W.Rudin,Real and Complex Analysis,Third edition,McGraw-Hill Book Co.,New York,1987.xiv+416 pp90

3.1.6 More books on real analysis90

3.1.7 Measure theory97

3.1.8 Analysis on general spaces100

3.1.9 G.Pólya,G.Szeg？,Problems and Theorems in Analysis.Vol.Ⅰ.Series,Integral calculus,Theory of Functions.Vol.Ⅱ.Theory of Functions,Zeros,Polynomials,Determinants,Number Theory,Geometry,Grundlehren der mathematischen Wissenschaften,Clas-sics in Mathematics,Springer-Verlag,Berlin,1998.xii+392 pp.xx+389 pp104

3.1.10 Orthogonal polynomials106

3.1.11 Problem books107

3.1.12 G.H.Hardy,J.E.Littlewood,G.Pólya,Inequalities,Reprint of the 1952 edition,Cambridge Mathematical Library,Cambridge Uni-versity Press,Cambridge,1988.xii+324 pp110

3.2 Complex analysis114

3.2.1 H.Cartan,Elementary Theory of Analytic Functions of One or Several Complex Variables. ？ditions Scientifiques Hermann,Paris;Addison-Wesley Publishing Co.,Inc.,Reading,Mass.-Palo Alto,Calif.-London,1963.22 8 pp115

3.2.2 L.Ahlfors,Complex Analysis,Third edition,International Series in Pure and Applied Mathematics,McGraw-Hill Book Co.,New York,1978.xi+331 pp115

3.2.3 R.Remmert,Theory of Complex Functions,Translated from the second German edition by Robert B.Burckel,Graduate Texts in Mathematics,122,Readings in Mathematics,Springer-Verlag,New York,1991.xx+453 pp116

3.2.4 More books on complex analysis117

3.2.5 Analytic and meromorphic functions,and conformal maps121

3.2.6 Several complex variables123

3.2.7 Sheaf theories126

3.2.8 H.Weyl,The Concept of a Riemann Surface,Translated from the third German edition by Gerald R.MacLane,ADIWES Interna-tional Series in Mathematics,Addison-Wesley Publishing Co.,Inc.,Reading,Mass.-London,1964.xi+191 pp128

3.2.9 More books on Riemann surfaces130

3.2.10 Quasiconformal mappings132

3.2.11 Teichmüller theory135

3.3 Harmonic analysis140

3.3.1 Y.Katznelson,An Introduction to Harmonic Analysis,3rd Edition,Cambridge Mathematical Library,Cambridge University Press,2004.xviii+314 pp141

3.3.2 More books on harmonic analysis and Fourier series142

3.3.3 A.Zygmund,Trigonometric Series.2 nd ed.Vols.Ⅰ,Ⅱ.Cambridge University Press,New York,1959,Vol.Ⅰ.,xii+383 pp.;Vol.Ⅱ.vii+354 pp147

3.3.4 Potential theory149

3.3.5 J.Garnett,Bounded Analytic Functions,Pure and Applied Math-ematics,96,Academic Press,Inc.,New York-London,1981.xvi+467 pp152

3.3.6 More books on Hardy spaces and function spaces153

3.3.7 E.Stein,Singular Integrals and Differentiability Properties of Func-tions,Princeton Mathematical Series,No.30 ,Princeton University Press,1970,xiv+290 pp157

3.3.8 G.Folland,Harmonic Analysis in Phase Space,Annals of Math-ematics Studies,122,Princeton University Press,Princeton,N.J.,1989.x+277 pp160

3.3.9 I.Daubechies,Ten Lectures on Wavelets,CBMS-NSF Regional Conference Series in Applied Mathematics,61,Society for Indus-trial and Applied Mathematics(SIAM),Philadelphia,PA,1992.xx+357 pp160

3.4 Functional analysis and operator theory162

3.4.1 S.Banach,Theory of Linear Operations,Translated from the French by F.Jellett,With comments by A.Peczyski and Cz.Bessaga,North-Holland Mathematical Library,38,North-Holland Publish-ing Co.,Amsterdam,1987.x+237 pp163

3.4.2 More basic books on functional analysis164

3.4.3 More books on Banach spaces167

3.4.4 More books on Hilbert spaces169

3.4.5 L.Schwartz,Théorie des Distributions,Hermann,Paris,1966,xiii+420 pp171

3.4.6 I.M.Gel'fand,G.E.Shilov,Generalized Functions.Vol.1.Prop-erties and Operations,Vol.2.Spaces of Fundamental and Gen-eralized Functions,Vol.3.Theory of Differential Equations,I.M.Gel'fand,N.Ya.Vilenkin,Vol.4.Applications of Harmonic Anal-ysis,I.M.Gel'fand,M.I.Graev,N.Ya.Vilenkin,Vol.5.Integral Geometry and Representation Theory,Academic Press,New York-London,1964,xviii+423 pp.,x+261 pp.,x+222 pp.,xiv+384 pp.,xvii+449 pp172

3.4.7 K.Yosida,Functional analysis,reprint of the sixth(1980)edition.Classics in Mathematics,Springer-Verlag,Berlin,1995.xii+501 pp174

3.4.8 N.Dunford,J.Schwartz,Linear Operators,Part Ⅰ,General The-ory;Part Ⅱ,Spectral theory.Selfadjoint operators in Hilbert space.Part Ⅲ,Spectral operators,Wiley Classics Library,A Wiley-Interscience Publication,John Wiley ＆ Sons,Inc.,New York,1988.xiv+858 pp.,x+859-1923,xx+1925-2592175

3.4.9 Semigroups and functional analysis176

3.4.10 A.Connes,Noncommutative Geometry,Academic Press,Inc.,San Diego,CA,1994.xiv+661 pp178

3.4.11 Operator algebras179

3.4.12 H.Brezis,Analyse Fonctionnelle,Théorie et Applications,Collec-tion Mathématiques Appliquées pour la Matrise.Masson,Paris,1983.xiv+234 pp184

3.4.13 K.Deimling,Nonlinear Functional Analysis,Springer-Verlag,Berlin,1985.xiv+450 pp185

4 Algebra187

4.1 Abstract algebras and finite groups188

4.1.1 Linear algebra188

4.1.2 Advanced linear algebra and matrix algebra191

4.1.3 van der Waerden,Algebra.Vol.Ⅰ.,Algebra.Vol.Ⅱ.,Based in part on lectures by E.Artin and E.Noether,Translated from the fifth German edition by John R.Schulenberge,Springer-Verlag,New York,1991.xiv+265 pp.,xii+284 pp194

4.1.4 More books on abstract algebra196

4.1.5 I.R.Shafarevich,Basic Notions of Algebra,Springer,Berlin,1990;Springer-Verlag,Berlin,1997.iv+258 pp204

4.1.6 R.Carter,Simple Groups of Lie Type,Pure and Applied Math-ematics,Vol.28 ,Reprint of the 1972 original,Wiley Classics Li-brary,A Wiley-Interscience Publication,John Wiley ＆ Sons,Inc.,New York,1989.x+335 pp205

4.1.7 Finite groups206

4.1.8 Finite groups and their representation theories213

4.1.9 Representation theories and associate algebras214

4.1.10 Rings and modules216

4.2 Commutative algebras218

4.3 Homological algebra225

4.3.1 H.Cartan,S.Eilenberg,Homological Algebra,With an appendix by David A.Buchsbaum,Reprint of the 1956 original,Princeton Landmarks in Mathematics,Princeton University Press,Princeton,NJ,1999.xvi+390 pp226

4.3.2 More books on homological algebra and related subjects228

5 Geometry233

5.1 Differential geometry233

5.1.1 H.Hopf,Differential Geometry in the Large,Notes taken by Peter Lax and John Gray,With a preface by S.S.Chern,Lecture Notes in Mathematics,1000,Springer-Verlag,Berlin,1983.vii+184 pp234

5.1.2 Introduction to differential geometry and Riemannian geometry235

5.1.3 More advanced books on Riemannian geometry240

5.1.4 Special topics in differential geometry245

5.1.5 M.Gromov,Metric Structures for Riemannian and Non-Riemannian Spaces,Based on the 1981 French original,With appendices by M.Katz,P.Pansu and S.Semmes,Translated from the French by Sean Michael Bates,Progress in Mathematics,152,Birkh？user Boston,Inc.,Boston,MA,1999.xx+585 pp253

5.1.6 M.Bridson,A.Haefliger,Metric Spaces of Non-positive Curvature,Grundlehren der Mathematischen Wissenschaften,319,Springer-Verlag,Berlin,1999.xxii+643 pp255

5.1.7 S.Helgason,Differential Geometry,Lie Groups,and Symmetric Spaces,Corrected reprint of the 1978 original,Graduate Studies in Mathematics,34,American Mathematical Society,Providence,RI,2001.xxvi+641 pp256

5.2 Geometric analysis258

5.2.1 R.Schoen,S.T.Yau,Lectures on Differential Geometry,Interna-tional Press,1994.v+235 pp259

5.2.2 T.Aubin,Nonlinear Analysis on Manifolds,Monge Ampére equa-tions,Grundlehren der Mathematischen Wissenschaften,252,Springer-Verlag,New York,1982.xii+204 pp260

5.2.3 More books on geometric analysis260

5.2.4 M.Gromov,Partial Differential Relations,Ergebnisse der Mathe-matik und ihrer Grenzgebiete(3),9,Springer-Verlag,Berlin,1986.x+363 pp264

5.2.5 H.Federer,Geometric Measure Theory,Die Grundlehren der math-ematischen Wissenschaften,Band 153,Springer-Verlag New York Inc.,New York,1969,xiv+676 pp265

5.2.6 More books on geometric measure theory266

5.2.7 Calculus of variation267

5.2.8 Fractal geometry270

5.3 Complex geometry and complex analysis272

5.3.1 L.H？rmander,An Introduction to Complex Analysis in Several Variables,Third edition,North-Holland Publishing Co.,Amster-dam,1990.xii+254 pp272

5.3.2 More books on complex geometry273

5.3.3 C.L.Siegel,Topics in Complex Function Theory.Vol.Ⅰ.Elliptic Functions and Uniformization Theory.Vol.Ⅱ.Automorphic Func-tions and Abelian Integrals.Vol.Ⅲ.Abelian Functions and Mod-ular Functions of Several Variables,Interscience Tracts in Pure and Applied Mathematics,No.25 ,Wiley-Interscience,1969.ix+186 pp.,1988.xii+193 pp.,1989.x+244 pp276

5.4 Algebraic geometry277

5.4.1 A.Grothendieck,The ？léments de géométrie algébrique,Inst.Hautes ？tudes Sci.Publ.Math.,1960-1967279

5.4.2 I.Shafarevich,Basic Algebraic Geometry.1.Varieties in Projec-tive Space.2.Schemes and Complex Manifolds.Second edition,Springer-Verlag,Berlin,1994.xx+303 pp.,xiv+269 pp281

5.4.3 D.Mumford,The Red book of Varieties and Schemes,Second,ex-panded edition.Includes the Michigan lectures(1974) on curves and their Jacobians,With contributions by Enrico Arbarello.Lec-ture Notes in Mathematics,1358.Springer-Verlag,Berlin,1999.x+306 pp283

5.4.4 R.Hartshorne,Algebraic Geometry,Graduate Texts in Mathemat-ics,No.5 2,Springer-Verlag,New York-Heidelberg,1977.xvi+496 pp285

5.4.5 P.Griffiths,J.Harris,Principles of Algebraic Geometry,Pure and Applied Mathematics,Wiley-Interscience,New York,1978.xii+813 pp286

5.4.6 Introduction to algebraic geometry and algebraic curves288

5.4.7 Topology of algebraic varieties289

5.4.8 Symplectic geometry and symplectic topology290

5.4.9 D.Mumford,J.Fogarty,F.Kirwan,Geometric invariant theory,Third edition,Ergebnisse der Mathematik und ihrer Grenzgebiete(2),34,Springer-Verlag,Berlin,1994.xiv+292 pp293

5.4.10 Classification of varieties and moduli spaces294

5.4.11 Algebraic curves297

5.4.12 Algebraic surfaces299

5.4.13 W.Fulton,Intersection Theory,Second edition,Ergebnisse der Mathematik und ihrer Grenzgebiete.3.Folge,Springer-Verlag,Berlin,1998.xiv+470 pp302

5.4.14 R.Lazarsfeld,Positivity in Algebraic Geometry.Ⅰ.Classical Set-ting:Line Bundles and Linear Series;Ⅱ.Positivity for Vector Bun-dles,and Multiplier Ideals,Ergebnisse der Mathematik und ihrer Grenzgebiete.3.Folge,Springer-Verlag,Berlin,2004.xviii+387 pp.,xviii+385 pp305

5.4.15 Toric varieties306

5.5 Convex geometry and discrete geometry309

5.5.1 R.T.Rockafellar,Convex Analysis,Princeton Mathematical Se-ries,No.28 ,Princeton University Press,Princeton,N.J.,1970.xviii+451 pp309

5.5.2 Convex functions and convex geometry311

6 Topology315

6.1 More classical topology316

6.1.1 P.Alexandroff,H.Hopf,Topologie I.Berlin,Springer,1935.xiii+636 pp316

6.1.2 K.Kuratowski,Topology.Vol.Ⅰ.,Vol.Ⅱ.,New edition,Revised and augmented,Translated from the French by J.Jaworowski Aca-demic Press,New York-London;Pa？stwowe Wydawnictwo Naukowe,Warsaw,1966.xx+560 pp.,1968.xiv+608 pp318

6.1.3 More books on topology318

6.1.4 Fixed point theory321

6.1.5 Dimension theory322

6.2 Algebraic topology324

6.2.1 J.Milnor,J.Stasheff,Characteristic Classes,Annals of Mathe-matics Studies,No.7 6,Princeton University Press,1974.vii+331 pp324

6.2.2 S.Eilenberg,N.Steenrod,Foundations of Algebraic Topology,Prince-University Press,1952.xv+328 pp326

6.2.3 More books on algebraic topology326

6.2.4 D.Rolfsen,Knots and Links,Corrected reprint of the 1976 original,Mathematics Lecture Series,7,Publish or Perish,Inc.,Houston,TX,1990.xiv+439 pp329

6.2.5 More knots and their invariants books330

6.3 Generalized cohomology theory and homotopy theories332

6.3.1 J.Adams,Stable Homotopy and Generalised Homology,Chicago Lectures in Mathematics,University of Chicago Press,Chicago,Ill.-London,1974.x+373 pp332

6.3.2 K-theory333

6.3.3 K.Brown,Cohomology of Groups,Graduate Texts in Mathemat-ics,87,Corrected reprint of the 1982 original,Graduate Texts in Mathematics,87,Springer-Verlag,New York,1994.x+306 pp335

6.3.4 G.W.Whitehead,Elements of Homotopy Theory,Graduate Texts in Mathematics,61,Springer-Verlag,New York-Berlin,1978.xxi+744 pp337

6.4 Differential topology338

6.4.1 J.Milnor,Morse Theory,Based on lecture notes by M.Spivak and R.Wells,Annals of Mathematics Studies,No.5 1,Princeton University Press,Princeton,N.J.,1963.vi+153 pp339

6.4.2 Differential topology340

6.4.3 R.Bott,L.Tu,Differential Forms in Algebraic Topology,Graduate Texts in Mathematics,82,Springer-Verlag,New York-Berlin,1982.xiv+331 pp341

6.4.4 W.V.D.Hodge,The Theory and Applications of Harmonic Inte-grals,Reprint of the 1941 original,With a foreword by Michael Atiyah,Cambridge Mathematical Library,Cambridge University Press,Cambridge,1989.xiv+284 pp342

6.4.5 M.Goresky,R.MacPherson,Stratified Morse theory,Ergebnisseder Mathematik und ihrer Grenzgebiete(3),14,Springer-Verlag,Berlin,1988.xiv+272 pp343

6.5 Geometric topology345

6.5.1 W.Thurston,The Geometry and Topology of Three-Manifolds,Lecture notes at Princeton University,1978-1980345

6.5.2 Four dimensional manifolds350

6.5.3 Geometric topology and surgery theory351

7 Number theory355

7.1 Number theory356

7.1.1 G.H.Hardy,E.Wright,An Introduction to the Theory of Numbers,Sixth edition,Revised by D.R.Heath-Brown and J.H.Silverman,With a foreword by Andrew Wiles,Oxford University Press,Ox-ford,2008.xxii+621 pp356

7.1.2 Books on basic number theory357

7.1.3 H.Davenport.The Higher Arithmetic.An Introduction to the The-ory of Numbers,Eighth edition,With editing and additional ma-terial by James H.Davenport,Cambridge University Press,Cam-bridge,2008.x+239 pp361

7.1.4 H.Hasse,Number Theory,Translated from the third German edi-tion and with a preface by Horst Günter Zimmer.Grundlehre nder Mathematischen Wissenschaften,229.Springer-Verlag,Berlin-New York,1980.xvii+638 pp362

7.1.5 A.Borevich,I.Shafarevich,Number Theory,Translated from the Russian by Newcomb Greenleaf,Pure and Applied Mathematics,Vol.20 ,Academic Press,New York-London,1966,x+435 pp362

7.1.6 A.Y.Khinchin,Three Pearls of Number Theory,Translated from the Russian by F.Bagemihl,H.Komm,and W.Seidel,Reprint of the 1952 translation,Dover Publications,Inc.,Mineola,NY,1998.6 4 pp363

7.1.7 E.Artin,Galois Theory,Notre Dame Mathematical Lectures,No.2 ,Edited and with a supplemental chapter by Arthur N.Milgram,Reprint of the 1944 second edition,Dover Publications,Inc.,Mi-neola,N.Y.,1998.iv+82 pp364

7.2 Algebraic number theory365

7.2.1 D.Hilbert,The Theory of Algebraic Number Fields,Translated from the German and with a preface by Iain T.Adamson,With an introduction by Franz Lemmermeyer and Norbert Schappacher,Springer-Verlag,Berlin,1998.xxxvi+350 pp365

7.2.2 E.Hecke,Lectures on the Theory of Algebraic Numbers,Trans-lated from the German by George U.Brauer,Jay R.Goldman and R.Kotzen,Graduate Texts in Mathematics,77,Springer-Verlag,New York-Berlin,1981.xii+239 pp366

7.2.3 J.W.S.Cassels,A.Fr？hlich,Algebraic Number Theory,Proceed-ings of the instructional conference held at the University of Sus-sex,Brighton,September 1-17,1965,Academic Press,London;Thompson Book Co.,Inc.,Washington,D.C.,1967,xviii+366 pp367

7.2.4 S.Lang,Algebraic Number Theory,Second edition,Graduate Texts in Mathematics,110,Springer-Verlag,New York,1994.xiv+357 pp368

7.2.5 More books on algebraic number theory368

7.2.6 Computational algebraic number theory370

7.2.7 J.P.Serre.Local Fields.Translated from the French by Marvin Jay Greenberg,Graduate Texts in Mathematics,67,Springer-Verlag,New York-Berlin,1979.viii+241 pp371

7.2.8 Galois cohomology372

7.2.9 Geometry of numbers373

7.3 Analytic number theory374

7.3.1 E.C.Titchmarsh,The Theory of the Riemann Zeta-Function,Sec-ond edition.Edited and with a preface by D.R.Heath-Brown,The Clarendon Press,Oxford University Press,New York,1986.x+412 pp375

7.3.2 More books on the Riemann zeta function375

7.3.3 Analytic number theory377

7.3.4 Additive number theory380

7.3.5 Multiplicative number theory381

7.4 Transcendental number theory382

7.5 Arithmetic algebraic geometry384

7.5.1 G.Shimura,Introduction to the Arithmetic Theory of Automor-phic Functions,Iwanami Shoten,Publishers,Tokyo;Princeton Uni-versity Press,Princeton,N.J.,1971.xiv+267 pp384

7.5.2 J.P.Serre,A Course in Arithmetic,Translated from the French,Graduate Texts in Mathematics,No.7 ,Springer-Verlag,New York-Heidelberg,1973.viii+115 pp385

7.5.3 J.Silverman,The Arithmetic of Elliptic Curves,Graduate Texts in Mathematics,106,Second edition,Graduate Texts in Mathe-matics,106,Springer,Dordrecht,2009.xx+513 pp385

7.5.4 D.Mumford,Abelian Varieties.With appendices by C.P.Ra-manujam and Yuri Manin,Corrected reprint of the second(1974)edition,Tata Institute of Fundamental Research Studies in Math-ematics,5,Hindustan Book Agency,New Delhi,2008.xii+263 pp387

7.5.5 Abalian varieties and theta functions387

7.5.6 Diophantine geometry389

7.5.7 Etale cohomology390

7.5.8 Quadratic forms391

7.5.9 More books on number theory393

7.6 Modular forms and automorphic representations395

7.6.1 R.Fricke,F.Klein,Vorlesungen uber die Theorie der automorphen Funktionen.Band 1:Die gruppentheoretischen Grundlagen.Band Ⅱ:Die funktionentheoretischen Ausfhrungen und die Andwendun-gen. Bibliotheca Mathematica Teubneriana,Bande 3,4,John-son Reprint Corp.,New York;B.G.Teubner Verlagsgesellschaft,Stuttg art 1965.Band Ⅰ:xiv+634 pp.:Band Ⅱ: xiv+668 pp396

7.6.2 I.M.Gel'fand,M.Graev,I.I.Pyatetskii-Shapiro,Representation Theory and Automorphic Functions,W.B.Saunders Co.,Philadel-phia,Pa.-London-Toronto,Ont.19 69.xvi+426 pp399

7.6.3 H.Jacquet,R.Langlands,Automorphic Forms on GL(2),Lecture Notes in Mathematics,Vol.11 4,Springer-Verlag,Berlin-New York,1970.vii+548 pp400

7.6.4 More books on modular forms and automorphic forms401

7.6.5 R.Langlands,On the Functional Equations Satisfied by Eisenstein Series,Lecture Notes in Mathematics,Vol.5 44,Springer-Verlag,Berlin-New York,1976.v+337 pp402

7.6.6 A.Borel,W.Casselman,Automorphic Forms,Representations and L-functions.Part 1,Part 2,Proceedings of Symposia in Pure Mathematics,ⅩⅩⅩⅢ.American Mathematical Society,Providence,R.I.,1979.x+322 pp.,vii+382 pp403

7.6.7 More books on modular forms,automorphic representations and cohomology of arithmetic groups404

7.6.8 Hypergeometric series and theory of partitions405

8 Differential equations407

8.1 Ordinary differential equations407

8.1.1 E.Coddington,N.Levinson,Theory of Ordinary Differential Equa-tions,McGraw-Hill Book Company,Inc.,New York-Toronto-London,1955.xii+429 pp408

8.1.2 More books on ordinary differential equations409

8.1.3 V.I.Arnold,Ordinary Differential Equations,Translated from the third Russian edition by Roger Cooke,Springer Textbook,Springer-Verlag,Berlin,1992.33 4 pp410

8.1.4 More books on ordinary differential equations and dynamical systems411

8.2 Linear differential operators413

8.2.1 L.Evans,Partial Differential Equations,Graduate Studies in Math-ematics,19,Second edition,Graduate Studies in Mathematics,19,American Mathematical Society,Providence,RI,2010.xxii+749 pp413

8.2.2 L.H？rmander,Linear Partial Differential Operators,Springer Ver-lag,Berlin-New York,1976.vii+285 pp414

8.2.3 More books on linear differential equations416

8.2.4 Inverse problems418

8.2.5 Critical point theory and minimax methods419

8.2.6 D.Gilbarg,N.Trudinger,Elliptic Partial Differential Equations of Second Order,Reprint of the 1998 edition,Classics in Mathematics,Springer-Verlag,Berlin,2001.xiv+517 pp421

8.2.7 More books on elliptic differential equations421

8.2.8 Pseudodifferential operators423

8.2.9 Parabolic equations425

8.2.10 R.Adams,John J.H.Fournier,Sobolev Spaces,Second edition,Pure and Applied Mathematics(Amsterdam),140,Elsevier/Academic Press,Amsterdam,2003.xiv+305 pp427

8.2.11 More books on Sobolev spaces427

8.2.12 T.Kato,Perturbation Theory for Linear Operators,Reprint of the 1980 edition,Classics in Mathematics,Springer-Verlag,Berlin,1995428

8.3 Nonlinear differential equations429

8.3.1 More geometric nonlinear differential equations429

8.3.2 Nonlinear differential equations and fluid mechanics432

9 Lie theories439

9.1 Lie groups and Lie algebras440

9.1.1 C.Chevalley,Theory of Lie Groups.I,Fifteenth printing,Prince-ton Mathematical Series,8,Princeton Landmarks in Mathematics,Princeton University Press,Princeton,NJ,1999.xii+217 pp440

9.1.2 J.P.Serre,Complex Semisimple Lie Algebras,Translated from the French by G.A.Jones,Reprint of the 1987 edition,Springer Mono-graphs in Mathematics,Springer-Verlag,Berlin,2001.x+74 pp441

9.1.3 N.Bourbaki,Lie Groups and Lie Algebras.Chapters 4-6,Trans-lated from the 1968 French original by Andrew Pressley.Elements of Mathematics(Berlin),Springer-Verlag,Berlin,2002.xii+300 pp442

9.1.4 More books on Lie algebras and Lie groups443

9.1.5 A.Borel,Linear Algebraic Groups,Second edition,Graduate Texts in Mathematics,126,Springer-Verlag,New York,1991.xii+288 pp445

9.1.6 More books on algebraic groups,algebraic geometry and number theory446

9.1.7 Algebraic invariant theories and representations of algebraic groups450

9.1.8 E.Artin,Geometric Algebra,Reprint of the 1957 original,Wiley Classics Library,A Wiley-Interscience Publication,John Wiley＆Sons,Inc.,New York,1988.x+214 pp452

9.1.9 J.Tits,Buildings of Spherical Type and Finite BN-pairs,Lecture Notes in Mathematics,Vol.38 6,Springer-Verlag,Berlin-New York,1974.x+299 pp453

9.1.10 More books on buildings and finite geometries454

9.1.11 Applications of Lie theories to differential equations457

9.1.12 Discrete subgroups of Lie groups and algebraic groups463

9.1.13 J.P.Serre,Trees,Translated from the French by John Stillwell,Springer-Verlag,Corrected 2nd printing of the 1980 English trans-lation,Springer Monographs in Mathematics,Springer-Verlag,Berlin,2003.x+142 pp466

9.1.14 Discrete subgroups of low rank Lie groups and algebraic groups467

9.1.15 Combinatorial groups and geometric group theory469

9.1.16 Coxeter groups474

9.1.17 Transformation groups475

9.1.18 V.Kac,Infinite-dimensional Lie Algebras,Third edition,Cam-bridge University Press,Cambridge,1990.xxii+400 pp479

9.1.19 Loop groups,quantum groups,Hopf algebras and vertex operator algebras479

9.1.20 Applications of Lie groups in sciences482

9.2 Representation theory483

9.2.1 J.P.Serre,Linear Representations of Finite Groups,Translated from the second French edition by Leonard L.Scott,Graduate Texts in Mathematics,Vol.42 ,Springer-Verlag,New York-Heidelberg,1977.x+170 pp484

9.2.2 I.G.Macdonald,Symmetric Functions and Hall Polynomials,Ox-ford Mathematical Monographs,The Clarendon Press,Oxford Uni-versity Press,New York,1979.viii+180 pp484

9.2.3 Representation theory of the symmetric group485

9.2.4 H.Weyl,The Classical Groups.Their Invariants and Represen-tations,Fifteenth printing,Princeton Landmarks in Mathematics,Princeton University Press,Princeton,NJ,1997.xiv+320 pp487

9.2.5 Representation theories of Lie groups489

10 Mathematical physics,dynamical systems and ergodic theory495

10.1 Classical mathematical physics495

10.1.1 R.Courant,D.Hilbert,Methods of Mathematical Physics.Vol.Ⅰ.,Vol.Ⅱ.,Interscience Publishers,Inc.,New York,1953.xv+561 pp..19 62.xxii+830 pp496

10.1.2 H.Wleyl,The Theory of Groups and Quantum Mechanics,from the 2d rev.,German ed.,by H.P.Robertson,Dover Publications,1949.44 8 pp497

10.1.3 L.D.Landau,E.M.Lifshitz,Course of Theoretical Physics.Vol.1.Mechanics,Third edition,Pergamon Press,Oxford-New York-Toronto,Ont.,1976.xxvii+169 pp499

10.2 More modern mathematical physics503

10.2.1 General relativity and gravitation503

10.2.2 S.Hawking,G.Ellis,The Large Scale Structure of Space-time,Cambridge Monographs on Mathematical Physics,No.1 ,Cam-bridge University Press,London-New York,1973.xi+391 pp506

10.2.3 Statistical mechanics509

10.2.4 Quantum field theory511

10.2.5 V.I.Arnold,Mathematical Methods of Classical Mechanics,Second edition,Graduate Texts in Mathematics,60,Springer-Verlag,New York,1989.xvi+508 pp512

10.2.6 M.Reed,B.Simon,Methods of Modern Mathematical Physics.I.Functional Analysis.Second edition;Ⅱ.Fourier Analysis,Self-adjointness;Ⅲ.Methods of Modern Mathematical Physics;Ⅳ.Analysis of Operators,Academic Press,Inc.,New York,1980.xv+400 pp.,1975.xv+361 pp.,1979.xv+463 pp.,1978.xv+396 pp514

10.2.7 Scattering theory515

10.3 Dynamical systems518

10.3.1 Dynamics and celestial mechanics518

10.3.2 Dynamical systems519

10.3.3 Infinite-dimensional dynamical systems526

10.3.4 R.Thom,Structural Stability and Morphogenesis.An Outline of a General Theory of Models.Translated from the French by D.H.Fowler.With a foreword by C.H.Waddington,Advanced Book Classics,Addison-Wesley Publishing Company,Advanced Book Program,Redwood City,CA,1989.xxxvi+348 pp529

10.3.5 Functional-differential equations530

10.3.6 Complex dynamics530

10.4 Ergodic theory533

11 Discrete mathematics and combinatorics537

11.1 Combinatorics537

11.1.1 R.Stanley,Enumerative Combinatorics,Vol.Ⅰ.,Vol.2.,With a foreword by Gian-Carlo Rota,The Wadsworth＆Brooks/Cole Mathematics Series,1986.xiv+306 pp.,1999.xii+581 pp538

11.1.2 Ploytopes,convex polytopes and geometric arrangements539

11.1.3 Gr？bner bases541

11.1.4 Matroid theory542

11.1.5 L.Lovász.Combinatorial Problems and Exercises,Corrected reprint of the 1993 second edition,AMS Chelsea Publishing,Providence,RI,2007.6 42 pp544

11.2 Discrete mathematics545

11.2.1 J.Conway,N.Sloane,Sphere Packings,Lattices and Groups,Third edition,With additional contributions by E.Bannai,R.E.Borcherds,J.Leech,S.P.Norton,A.M.Odlyzko,R.A.Parker,L.Queen and B.B.Venkov,Grundlehren der Mathematischen Wissenschaften,290.Springer-Verlag,New York,1999.lxxiv+703 pp545

11.2.2 Graph theory546

11.2.3 Graphs and their spectra551

11.2.4 Random graphs552

12 Probability and applications553

12.1 Probability553

12.1.1 A.N.Kolmogorov,Foundations ofthe Theory ofProbability,Trans-lation edited by Nathan Morrison,with an added bibliography by A.T.Bharucha-Reid,Chelsea Publishing Co.,New York,1956.viii+84 pp.Translation of Grundbegriffe der Wahrscheinlichkeits-rechnung,Springer,Berlin,1933554

12.1.2 W.Feller,An Introduction to Probability Theory and its Applica-tions,Vol.Ⅰ,Vol.Ⅱ.Third edition,John Wiley＆Sons,Inc.,New York-London-Sydney,1968.xviii+509 pp.,1971,xxiv+669 pp555

12.1.3 More classical books on probability556

12.1.4 More modern books on probability558

12.1.5 Probability and analysis559

12.1.6 More specialized books in probability560

12.1.7 Random walks562

12.2 Stochastic analysis564

12.2.1 J.L.Doob,Stochastic Processes,Reprint of the 1953 original,Wiley Classics Library,A Wiley-Interscience Publication,John Wiley＆Sons,Inc.,New York,1990.viii+654 pp565

12.2.2 Brownian motions and stochastic processes567

12.2.3 Stochastic calculus and equations572

12.2.4 Large deviations574

12.2.5 Malliavin calculus575

12.3 Applications of probability576

12.3.1 Probabilistic methods and applications576

12.3.2 Random matrices580

13 Foundations of math,computer science,numerical math583

13.1 Mathematical logic583

13.1.1 Mathematical logic584

13.1.2 D.Hofstadter,G？del,Escher,Bach:an Eternal Golden Braid,Basic Books,Inc.,Publishers,New York,1979.xxi+777 pp586

13.1.3 B.Russell,Introduction to Mathematical Philosophy,Reprint of the 1920 second edition,Dover Publications,Inc.,New York,1993.viii+208 pp586

13.1.4 Set theory587

13.1.5 Model theory,non-standard analysis,recursive functions591

13.2 Computer science594

13.2.1 D.Knuth,The Art of Computer Programming.Vol.1 -Ⅳ,Second printing,Addison-Wesley Publishing Co.,1969.xxi+634 pp595

13.2.2 R.Graham,D.Knuth,O.Patashnik,Concrete Mathematics.A Foundation for Computer Science,Second edition,Addison-Wesley Publishing Company,Reading,MA,1994.xiv+657 pp595

13.2.3 T.Cover,J.Thomas,Elements of Information Theory,Second edi-tion,Wiley-Interscience[John Wiley＆Sons],Hoboken,NJ,2006.xxiv+748 pp596

13.2.4 N.Wiener,Cybernetics,or Control and Communication in the An-imal and the Machine,Actualités Sci.Ind.,no.10 53,Hermann et Cie.,Paris;The Technology Press,Cambridge,Mass.;John Wiley＆Sons,Inc.,New York,1948.19 4 pp597

13.2.5 M.Petkovsek,H.Wilf,D.Zeilberger,A=B,With a foreword by Donald E.Knuth,With a separately available computer disk,A K Peters,Ltd.,Wellesley,MA,1996.xii+212 pp599

13.2.6 I.MacWilliams,N.Sloane,The Theory of Error-correcting Codes,Ⅰ,Ⅱ,North-Holland Mathematical Library,Vol.16.North-Holland Publishing Co.,Amsterdam-New York-Oxford,1977.pp.i-xv and 1-369.pp.i-ix and 370-762600

13.2.7 More books on coding theory601

13.2.8 Algorithm and automata602

13.3 Game theory and optimization604

13.3.1 J.von Neumann,O.Morgenstern,Theory of Games and Economic Behavior,Fourth printing of the 2004 sixtieth-anniversary edition,With an introduction by Harold W.Kuhn and an afterword by Ariel Rubinstein,Princeton University Press,Princeton,NJ,2007.xxxii+739 pp605

13.3.2 More books on game theory and optimization606

13.4 Numerical analysis and matrix computation610

13.4.1 Numerical analysis611

13.4.2 Finite element methods and finite difference methods617

13.4.3 Approximation theory620

Appendix A:Books in Chinese version623

Appendix B:Books reprinted in the mainland of China631

Index of books643