數學研究生教材（，簡稱 GTM）是由施普林格出版的一系統研究所程度之數學教科書。這一系列的書與施普林格其他數學系列的書一樣，都是具相同尺寸的黃色封面書籍。GTM 系列的書在封面上端都會有一段白底黃字的字樣，標示著「Graduate Texts in Mathematics」。 這一系列的書會偏向於寫成較性質相似的數學大學生教材系列還要困難，雖然這兩個系列有許多部分重疊，不論是在其所涉及之材料，或是在其難易程度。 書目列表 Introduction to Axiomatic Set Theory Gaisi Takeuti Wilson M Zaring 1982 2nd ed Measure and Category A Survey of the Analogies between Topological and Measure Spaces John C Oxtoby 1980 2nd ed Topological Vector Spaces H H Schaefer M P Wolff 1999 2nd ed A Course in Homological Algebra Peter Hilton Urs Stammbach 1997 2nd ed Categories for the Working Mathematician Saunders Mac Lane 1998 2nd ed Projective Planes Daniel R Hughes Fred C Piper 1982 A Course in Arithmetic JeanPierre Serre 1996 Axiomatic Set Theory Gaisi Takeuti Wilson M Zaring 1973 Introduction to Lie Algebras and Representation Theory James E Humphreys 1997 A Course in SimpleHomotopy Theory Marshall M Cohen 1973 Functions of One Complex Variable I John B Conway 1978 2nd ed Advanced Mathematical Analysis Richard Beals 1973 Rings and Categories of Modules Frank W Anderson Kent R Fuller 1992 2nd ed Stable Mappings and Their Singularities Martin Golubitsky Victor Guillemin 1974 Lectures in Functional Analysis and Operator Theory Sterling K Berberian 1974 The Structure of Fields David J Winter 1974 Random Processes Murray Rosenblatt 1974 Measure Theory Paul R Halmos 1974 A Hilbert Space Problem Book Paul R Halmos 1982 2nd ed Fibre Bundles Dale Husemoller 1994 3rd ed Linear Algebraic Groups James E Humphreys 1998 An Algebraic Introduction to Mathematical Logic Donald W Barnes John M Mack 1975 Linear Algebra Werner H Greub 1981 Geometric Functional Analysis and Its Applications Richard B Holmes 1975 Real and Abstract Analysis Edwin Hewitt Karl Stromberg 1975 Algebraic Theories Ernest G Manes 1976 General Topology John L Kelley 1975 Commutative Algebra I Oscar Zariski Pierre Samuel Cohen 1975 Commutative Algebra II Oscar Zariski Pierre Samuel 1975 Lectures in Abstract Algebra I Basic Concepts Nathan Jacobson 1976 Lectures in Abstract Algebra II Linear Algebra Nathan Jacobson 1984 Lectures in Abstract Algebra III Theory of Fields and Galois Theory Nathan Jacobson 1976 Differential Topology Morris W Hirsch 1976 Principles of Random Walk Frank Spitzer 2001 Several Complex Variables and Banach Algebras Herbert Alexander John Wermer 1998 3rd ed Linear Topological Spaces John L Kelley Isaac Namioka 1982 Mathematical Logic J Donald Monk 1976 Several Complex Variables H Grauert K Fritzsche 1976 An Invitation to CAlgebras William Arveson 1976 Denumerable Markov Chains John G Kemeny J Laurie Snell Anthony W Knapp DS Griffeath 1976 Modular Functions and Dirichlet Series in Number Theory Tom M Apostol 1989 2nd ed Linear Representations of Finite Groups JeanPierre Serre Leonhard L Scott 1977 Rings of Continuous Functions Leonard Gillman Meyer Jerison 1976 Elementary Algebraic Geometry Keith Kendig 1977 Also published from Dover Publications as the second edition 2015 Probability Theory I M Loève 1977 4th ed Probability Theory II M Loève 1978 4th ed Geometric Topology in Dimensions 2 and 3 Edwin E Moise 1977 General Relativity for Mathematicians R K Sachs H Wu 1983 Linear Geometry K W Gruenberg A J Weir 2010 Fermats Last Theorem A Genetic Introduction to Algebraic Number Theory Harold M Edwards 2000 A Course in Differential Geometry William Klingenberg D Hoffman 1983 Algebraic Geometry Robin Hartshorne 2010 A Course in Mathematical Logic for Mathematicians Yu I Manin Boris Zilber 2009 2nd ed Combinatorics with Emphasis on the Theory of Graphs Mark E Watkins Jack E Graver 1977 Introduction to Operator Theory I Elements of Functional Analysis Arlen Brown Carl Pearcy 1977 Algebraic Topology An Introduction William S Massey 1977 Introduction to Knot Theory Richard H Crowell Ralph H Fox 1977 padic Numbers padic Analysis and ZetaFunctions Neal Koblitz 1984 2nd ed Cyclotomic Fields Serge Lang 1978 Note that this volume of the series with volume 69 were combined as volume 121 Mathematical Methods of Classical Mechanics V I Arnold A Weinstein K Vogtmann 1989 2nd ed Elements of Homotopy Theory George W Whitehead 1978 Fundamentals of the Theory of Groups M I Kargapolov J I Merzljakov 1979 Graph Theory An Introductory Course Béla Bollobás 1979 Fourier Series A Modern Introduction Volume 1 R E Edwards 1979 2nd ed Differential Analysis on Complex Manifolds Raymond O Wells Jr 2008 3rd ed Introduction to Affine Group Schemes W C Waterhouse 1979 Local Fields JeanPierre Serre 1979 Linear Operators in Hilbert Spaces 1980 Cyclotomic Fields II Serge Lang 1980 Singular Homology Theory William S Massey 1980 Riemann Surfaces Irwin Kra 1992 2nd ed Classical Topology and Combinatorial Group Theory John Stillwell 1980 2ed 1993 Algebra Thomas W Hungerford 1974 Multiplicative Number Theory Harold Davenport Hugh Montgomery 2000 3rd ed Basic Theory of Algebraic Groups and Lie Algebras G P Hochschild 1981 Algebraic Geometry An Introduction to Birational Geometry of Algebraic Varieties Shigeru Iitaka 1982 Lectures on the Theory of Algebraic Numbers E T Hecke 1981 A Course in Universal Algebra Burris Stanley and Sankappanavar H P Online 1981 An Introduction to Ergodic Theory Peter Walters 1982 A Course in the Theory of Groups 1996 2nd ed Lectures on Riemann Surfaces 1981 Differential Forms in Algebraic Topology Raoul Bott Loring W Tu 1982 Introduction to Cyclotomic Fields Lawrence C Washington 1997 2nd ed A Classical Introduction to Modern Number Theory Kenneth Ireland Michael Rosen 1990 2nd ed Fourier Series A Modern Introduction Volume 2 R E Edwards 1982 2nd ed Introduction to Coding Theory J H van Lint 3rd ed 1998 Cohomology of Groups Kenneth S Brown 1982 Associative Algebras R S Pierce 1982 Introduction to Algebraic and Abelian Functions Serge Lang 1982 2nd ed An Introduction to Convex Polytopes Arne Brondsted 1983 The Geometry of Discrete Groups 1983 2nd print 1995 Sequences and Series in Banach Spaces J Diestel 1984 Modern Geometry Methods and Applications Part I The Geometry of Surfaces Transformation Groups and Fields B A Dubrovin Anatoly Timofeevich Fomenko Sergei Novikov 1992 2nd ed Foundations of Differentiable Manifolds and Lie Groups 1983 Probability1 Albert N Shiryaev 2016 3rd ed A Course in Functional Analysis John B Conway 2007 2nd ed Introduction to Elliptic Curves and Modular Forms Neal I Koblitz 1993 2nd ed Representations of Compact Lie Groups 1985 Finite Reflection Groups LC Grove CT Benson 1985 2nd ed Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions Christian Berg Jens Peter Reus Christensen Paul Ressel 1984 Galois Theory Harold M Edwards 1984 Lie Groups Lie Algebras and Their Representations V S Varadarajan 1984 Complex Analysis Serge Lang 1999 4th ed Modern Geometry Methods and Applications Part II The Geometry and Topology of Manifolds B A Dubrovin Anatoly Timofeevich Fomenko Sergei Novikov 1985 SL2 R Serge Lang 1985 The Arithmetic of Elliptic Curves Joseph H Silverman 2009 2nd ed Applications of Lie Groups to Differential Equations Peter J Olver 2ed 1993 Holomorphic Functions and Integral Representations in Several Complex Variables R Michael Range 1986 Univalent Functions and Teichmüller Spaces O Lehto 1987 Algebraic Number Theory Serge Lang 1994 2nd ed Elliptic Curves 2004 2nd ed Elliptic Functions Serge Lang 1987 2nd ed Brownian Motion and Stochastic Calculus Ioannis Karatzas Steven Shreve 2ed 2000 A Course in Number Theory and Cryptography Neal Koblitz 2ed 1994 Differential Geometry Manifolds Curves and Surfaces Marcel Berger Bernard Gostiaux 1988 Measure and Integral Volume 1 John L Kelley TP Srinivasan 1988 Algebraic Groups and Class Fields JeanPierre Serre 1988 Analysis Now Gert K Pedersen 1989 An Introduction to Algebraic Topology Joseph J Rotman 1988 Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation William P Ziemer 1989 Cyclotomic Fields I and II Serge Lang 1990 Combined 2nd ed Originally published as volumes 59 and 69 in this series Theory of Complex Functions Reinhold Remmert 1991 Numbers HeinzDieter Ebbinghaus et al 1990 Modern Geometry Methods and Applications Part III Introduction to Homology Theory B A Dubrovin Anatoly Timofeevich Fomenko Sergei Novikov 1990 Complex Variables An Introduction Carlos A Berenstein Roger Gay 1991 A companion volume by the same authors Complex Analysis and Special Topics in Harmonic Analysis 1995 Linear Algebraic Groups Armand Borel 1991 A Basic Course in Algebraic Topology William S Massey 1991 Partial Differential Equations Jeffrey Rauch 1991 Representation Theory William Fulton Joe Harris 1991 Tensor Geometry The Geometric Viewpoint and its Uses Christopher T J Dodson Timothy Poston 1991 2nd ed A First Course in Noncommutative Rings T Y Lam 2001 2nd ed Iteration of Rational Functions Complex Analytic Dynamical Systems Alan F Beardon 1991 Algebraic Geometry Joe Harris 1992 Coding and Information Theory Steven Roman 1992 Advanced Linear Algebra Steven Roman 2008 3rd ed Algebra An Approach via Module Theory William Adkins Steven Weintraub 1992 Harmonic Function Theory Sheldon Axler Paul Bourdon Wade Ramey 2001 2nd ed A Course in Computational Algebraic Number Theory Henri Cohen 1996 Topology and Geometry Glen E Bredon 1993 Optima and Equilibria JeanPierre Aubin 1998 Gröbner Bases A Computational Approach to Commutative Algebra Thomas Becker Volker Weispfenning 1993 Real and Functional Analysis Serge Lang 1993 3rd ed Measure Theory J L Doob 1994 Noncommutative Algebra Benson Farb R Keith Dennis 1993 Homology Theory An Introduction to Algebraic Topology James W Vick 1994 2nd ed Computability A Mathematical Sketchbook Douglas S Bridges 1994 Algebraic KTheory and Its Applications Jonathan Rosenberg 1994 An Introduction to the Theory of Groups Joseph J Rotman 1995 4th ed Foundations of Hyperbolic Manifolds John G Ratcliffe 2006 2nd ed Commutative Algebra with a View Toward Algebraic Geometry David Eisenbud 1995 Advanced Topics in the Arithmetic of Elliptic Curves Joseph H Silverman 1994 This volume is subsequent to volume 106 in this series Lectures on Polytopes Günter M Ziegler 1995 Algebraic Topology A First Course William Fulton 1995 An Introduction to Analysis Arlen Brown Carl Pearcy 1995 Quantum Groups Christian Kassel 1995 Classical Descriptive Set Theory Alexander S Kechris 1995 Integration and Probability Paul Malliavin 1995 The problems and workedout solutions book for all the exercises Exercises and Solutions Manual for Integration and Probability by Paul Malliavin Gerard Letac 1995 Field Theory Steven Roman 2006 2nd ed Functions of One Complex Variable II John B Conway 1995 Differential and Riemannian Manifolds Serge Lang 1995 Polynomials and Polynomial Inequalities Peter Borwein Tamas Erdelyi 1995 Groups and Representations J L Alperin Rowen B Bell 1995 Permutation Groups John D Dixon Brian Mortimer 1996 Additive Number Theory The Classical Bases Melvyn B Nathanson 1996 Additive Number Theory Inverse Problems and the Geometry of Sumsets Melvyn B Nathanson 1996 Differential Geometry Cartans Generalization of Kleins Erlangen Program R W Sharpe 1997 Field and Galois Theory Patrick Morandi 1996 Combinatorial Convexity and Algebraic Geometry Guenter Ewald 1996 Matrix Analysis Rajendra Bhatia 1997 Sheaf Theory Glen E Bredon 1997 2nd ed Riemannian Geometry Peter Petersen 2016 3rd ed Classical Topics in Complex Function Theory Reinhold Remmert 1998 Graph Theory 2017 5th ed Foundations of Real and Abstract Analysis Douglas S Bridges 1998 An Introduction to Knot Theory W B Raymond Lickorish 1997 Introduction to Riemannian Manifolds John M Lee 2018 2nd ed The first edition is Riemannian Manifolds An Introduction to Curvature Analytic Number Theory Donald J Newman 1998 Nonsmooth Analysis and Control Theory Francis H Clarke Yuri S Ledyaev Ronald J Stern Peter R Wolenski 1998 Banach Algebra Techniques in Operator Theory Ronald G Douglas 1998 2nd ed A Course on Borel Sets S M Srivastava 1998 Numerical Analysis Rainer Kress 1998 Ordinary Differential Equations Wolfgang Walter 1998 An Introduction to Banach Space Theory Robert E Megginson 1998 Modern Graph Theory Béla Bollobás 1998 Using Algebraic Geometry David A Cox John Little Donal OShea 2005 2nd ed Fourier Analysis on Number Fields Dinakar Ramakrishnan Robert J Valenza 1999 Moduli of Curves Joe Harris Ian Morrison 1998 Lectures on the Hyperreals Robert Goldblatt 1998 Lectures on Modules and Rings TsitYuen Lam 1999 Problems in Algebraic Number Theory M Ram Murty Jody Indigo Esmonde 2005 2nd ed Fundamentals of Differential Geometry Serge Lang 1999 Elements of Functional Analysis Francis Hirsch Gilles Lacombe 1999 Advanced Topics in Computational Number Theory Henri Cohen 2000 OneParameter Semigroups for Linear Evolution Equations Engel Nagel 2000 Elementary Methods in Number Theory Melvyn B Nathanson 2000 Basic Homological Algebra M Scott Osborne 2000 The Geometry of Schemes Eisenbud Joe Harris 2000 A Course in padic Analysis Alain M Robert 2000 Theory of Bergman Spaces Hakan Hedenmalm Boris Korenblum Kehe Zhu 2000 An Introduction to RiemannFinsler Geometry David Bao ShiingShen Chern Zhongmin Shen 2000 Diophantine Geometry Marc Hindry Joseph H Silverman 2000 Introduction to Topological Manifolds John M Lee 2011 2nd ed The Symmetric Group Representations Combinatorial Algorithms and Symmetric Functions Bruce E Sagan 2001 2nd ed Galois Theory JeanPierre Escofier 2001 Rational Homotopy Theory Yves Félix Stephen Halperin JeanClaude Thomas 2000 Problems in Analytic Number Theory M Ram Murty 2007 2nd ed Algebraic Graph Theory Chris Godsil Gordon Royle 2001 Analysis for Applied Mathematics Ward Cheney 2001 A Short Course on Spectral Theory William Arveson 2002 Number Theory in Function Fields Michael Rosen 2002 Algebra Serge Lang 2002 Revised 3rd ed Lectures on Discrete Geometry Jiří Matoušek 2002 From Holomorphic Functions to Complex Manifolds Hans Grauert 2002 Partial Differential Equations Jürgen Jost 2013 3rd ed Algebraic Functions and Projective Curves David M Goldschmidt 2003 Matrices Theory and Applications Denis Serre 2010 2nd ed Model Theory An Introduction David Marker 2002 Introduction to Smooth Manifolds John M Lee 2012 2nd ed The Arithmetic of Hyperbolic 3Manifolds Colin Maclachlan Alan W Reid 2003 Smooth Manifolds and Observables Jet Nestruev 2003 Convex Polytopes Branko Grünbaum 2003 Lie Groups Lie Algebras and Representations An Elementary Introduction Brian C Hall 2015 2nd ed Fourier Analysis and its Applications Anders Vretblad 2003 Metric Structures in Differential Geometry Walschap G 2004 Lie Groups Daniel Bump 2013 2nd ed Spaces of Holomorphic Functions in the Unit Ball Kehe Zhu 2005 Combinatorial Commutative Algebra Ezra Miller Bernd Sturmfels 2005 A First Course in Modular Forms Fred Diamond J Shurman 2006 The Geometry of Syzygies David Eisenbud 2005 An Introduction to Markov Processes Daniel W Stroock 2014 2nd ed Combinatorics of Coxeter Groups Anders Björner Francisco Brenti 2005 An Introduction to Number Theory Everest G Ward T 2005 Topics in Banach Space Theory Albiac F Kalton N J 2016 2nd ed Analysis and Probability Wavelets Signals Fractals Jorgensen P E T 2006 Compact Lie Groups M R Sepanski 2007 Bounded Analytic Functions Garnett J 2007 An Introduction to Operators on the HardyHilbert Space Ruben A MartinezAvendano Peter Rosenthal 2007 A Course in Enumeration Aigner M 2007 Number Theory Volume I Tools and Diophantine Equations Cohen H 2007 Number Theory Volume II Analytic and Modern Tools Cohen H 2007 The Arithmetic of Dynamical Systems Joseph H Silverman 2007 Abstract Algebra Grillet Pierre Antoine 2007 Topological Methods in Group Theory Geoghegan Ross 2007 Graph Theory Adrian Bondy USR Murty 2008 Complex Analysis Introduced in the Spirit of Lipman Bers Gilman Jane P Kra Irwin Rodriguez Rubi E 2007 A Course in Commutative Banach Algebras Kaniuth Eberhard 2008 Braid Groups Kassel Christian Turaev Vladimir 2008 Buildings Theory and Applications Abramenko Peter Brown Ken 2008 Classical Fourier Analysis Loukas Grafakos 2014 3rd ed Modern Fourier Analysis Loukas Grafakos 2014 3rd ed The Finite Simple Groups Robert A Wilson 2009 Distributions and Operators Gerd Grubb 2009 Elementary Functional Analysis MacCluer Barbara D 2009 Algebraic Function Fields and Codes 2009 Symmetry Representations and Invariants Goodman Roe Wallach Nolan R 2009 A Course in Commutative Algebra Kemper Gregor 2010 Deformation Theory Robin Hartshorne 2010 Foundations of Optimization in Finite Dimensions Osman Guler 2010 Ergodic Theory with a view towards Number Theory Thomas Ward Manfred Einsiedler 2011 Monomial Ideals Jürgen Herzog Hibi Takayuki 2010 Probability and Stochastics Erhan Cinlar 2011 Essentials of Integration Theory for Analysis Daniel W Stroock 2012 Analysis on Fock Spaces Kehe Zhu 2012 Functional Analysis Calculus of Variations and Optimal Control Francis H Clarke 2013 Unbounded Selfadjoint Operators on Hilbert Space Konrad Schmüdgen 2012 Calculus Without Derivatives JeanPaul Penot 2012 Quantum Theory for Mathematicians Brian C Hall 2013 Geometric Analysis of the Bergman Kernel and Metric Krantz Steven G 2013 Locally Convex Spaces M Scott Osborne 2014 Fundamentals of Algebraic Topology Steven Weintraub 2014 Integer Programming Michelangelo Conforti Gérard P Cornuéjols Giacomo Zambelli 2014 Operator Theoretic Aspects of Ergodic Theory Tanja Eisner Bálint Farkas Markus Haase Rainer Nagel 2015 Homotopical Topology Anatoly Fomenko Dmitry Fuchs 2016 2nd ed Brownian Motion Martingales and Stochastic Calculus JeanFrançois Le Gall 2016 Differential Geometry Connections Curvature and Characteristic Classes Loring W Tu 2017 Functional Analysis Spectral Theory and Applications Manfred Einsiedler Thomas Ward 2017 The Moment Problem Konrad Schmüdgen 2017 Modern Real Analysis William P Ziemer 2017 2nd ed Binomial Ideals Jürgen Herzog Takayuki Hibi Hidefumi Ohsugi 2018 Introduction to Real Analysis Christopher Heil 2019 Intersection Homology Perverse Sheaves with Applications to Singularities Laurenţiu G Maxim 2019 Measure Integration Real Analysis Sheldon Axler 2020 Basic Representation Theory of Algebras Ibrahim Assem Flávio U Coelho 2020 Spectral Theory David Borthwick 2020 An Invitation to Unbounded Representations of Algebras on Hilbert Space Konrad Schmüdgen 2020 Lectures on Convex Geometry Daniel Hug Wolfgang Weil 2020 Explorations in Complex Functions Richard Beals Roderick S C Wong 2020 Quaternion Algebras John Voight 2020 Ergodic Dynamics From Basic Theory to Applications Jane M Hawkins 2020 Lessons in Enumerative Combinatorics Omer Egecioglu Adriano Garsia 2021 Mathematical Logic HeinzDieter Ebbinghaus Jörg Flum Wolfgang Thomas 2021 3rd ed Random Walk Brownian Motion and Martingales Rabi Bhattacharya Edward C Waymire 2021 Stationary Processes and Discrete Parameter Markov Processes Rabi Bhattacharya Edward C Waymire 2022 Partial Differential Equations Wolfgang Arendt Karsten Urban 2023 Measure Theory Probability and Stochastic Processes JeanFrançois Le Gall 2022 Drinfeld Modules Mihran Papikian 2023 另見 數學大學生教材 註釋 外部連結 分類：數學叢書 分類：數學教科書