Graduate Texts in Mathematics


Graduate Texts in Mathematics is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size. The GTM series is easily identified by a white band at the top of the book.
The books in this series tend to be written at a more advanced level than the similar Undergraduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level.

List of books

  1. Introduction to Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring
  2. Measure and Category - A Survey of the Analogies between Topological and Measure Spaces, John C. Oxtoby
  3. Topological Vector Spaces, H. H. Schaefer, M. P. Wolff
  4. A Course in Homological Algebra, Peter Hilton, Urs Stammbach
  5. Categories for the Working Mathematician, Saunders Mac Lane
  6. Projective Planes, Daniel R. Hughes, Fred C. Piper,
  7. A Course in Arithmetic, Jean-Pierre Serre
  8. Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring,
  9. Introduction to Lie Algebras and Representation Theory, James E. Humphreys
  10. A Course in Simple-Homotopy Theory, Marshall. M. Cohen,
  11. Functions of One Complex Variable I, John B. Conway
  12. Advanced Mathematical Analysis, Richard Beals
  13. Rings and Categories of Modules, Frank W. Anderson, Kent R. Fuller
  14. Stable Mappings and Their Singularities, Martin Golubitsky, Victor Guillemin,
  15. Lectures in Functional Analysis and Operator Theory, Sterling K. Berberian,
  16. The Structure of Fields, David J. Winter,
  17. Random Processes, Murray Rosenblatt,
  18. Measure Theory, Paul R. Halmos
  19. A Hilbert Space Problem Book, Paul R. Halmos
  20. Fibre Bundles, Dale Husemoller
  21. Linear Algebraic Groups, James E. Humphreys
  22. An Algebraic Introduction to Mathematical Logic, Donald W. Barnes, John M. Mack
  23. Linear Algebra, Werner H. Greub
  24. Geometric Functional Analysis and Its Applications, Richard B. Holmes,
  25. Real and Abstract Analysis, Edwin Hewitt, Karl Stromberg
  26. Algebraic Theories, Ernest G. Manes,
  27. General Topology, John L. Kelley
  28. Commutative Algebra I, Oscar Zariski, Pierre Samuel
  29. Commutative Algebra II, Oscar Zariski, Pierre Samuel
  30. Lectures in Abstract Algebra I: Basic Concepts, Nathan Jacobson
  31. Lectures in Abstract Algebra II: Linear Algebra, Nathan Jacobson
  32. Lectures in Abstract Algebra III: Theory of Fields and Galois Theory, Nathan Jacobson
  33. Differential Topology, Morris W. Hirsch
  34. Principles of Random Walk, Frank Spitzer
  35. Several Complex Variables and Banach Algebras, Herbert Alexander, John Wermer
  36. Linear Topological Spaces, John L. Kelley, Isaac Namioka
  37. Mathematical Logic, J. Donald Monk
  38. Several Complex Variables, H. Grauert, K. Fritzsche
  39. An Invitation to -Algebras, William Arveson
  40. Denumerable Markov Chains, John G. Kemeny, J. Laurie Snell, Anthony W. Knapp, D.S. Griffeath
  41. Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol
  42. Linear Representations of Finite Groups, Jean-Pierre Serre, Leonhard L. Scott
  43. Rings of Continuous Functions, Leonard Gillman, Meyer Jerison
  44. Elementary Algebraic Geometry, Keith Kendig
  45. Probability Theory I, M. Loève
  46. Probability Theory II, M. Loève
  47. Geometric Topology in Dimensions 2 and 3, Edwin E. Moise
  48. General Relativity for Mathematicians, R. K. Sachs, H. Wu
  49. Linear Geometry, K. W. Gruenberg, A. J. Weir
  50. Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory, Harold M. Edwards
  51. A Course in Differential Geometry, William Klingenberg, D. Hoffman
  52. Algebraic Geometry, Robin Hartshorne
  53. A Course in Mathematical Logic for Mathematicians, Yu. I. Manin, Boris Zilber
  54. Combinatorics with Emphasis on the Theory of Graphs, Mark E. Watkins, Jack E. Graver
  55. Introduction to Operator Theory I: Elements of Functional Analysis, Arlen Brown, Carl Pearcy
  56. Algebraic Topology: An Introduction, William S. Massey
  57. Introduction to Knot Theory, Richard H. Crowell, Ralph H. Fox
  58. p-adic Numbers, p-adic Analysis, and Zeta-Functions, Neal Koblitz
  59. Cyclotomic Fields, Serge Lang
  60. Mathematical Methods of Classical Mechanics, V. I. Arnold, A. Weinstein, K. Vogtmann
  61. Elements of Homotopy Theory, George W. Whitehead
  62. Fundamentals of the Theory of Groups, M. I. Kargapolov, J. I. Merzljakov
  63. Graph Theory - An Introductory Course, Béla Bollobás
  64. Fourier Series - A Modern Introduction Volume 1, R. E. Edwards
  65. Differential Analysis on Complex Manifolds, Raymond O. Wells, Jr.
  66. Introduction to Affine Group Schemes, W. C. Waterhouse
  67. Local Fields, Jean-Pierre Serre
  68. Linear Operators in Hilbert Spaces,
  69. Cyclotomic Fields II, Serge Lang
  70. Singular Homology Theory, William S. Massey
  71. Riemann Surfaces,, Irwin Kra
  72. Classical Topology and Combinatorial Group Theory, John Stillwell
  73. Algebra, Thomas W. Hungerford
  74. Multiplicative Number Theory, Harold Davenport, Hugh Montgomery
  75. Basic Theory of Algebraic Groups and Lie Algebras, G. P. Hochschild
  76. Algebraic Geometry - An Introduction to Birational Geometry of Algebraic Varieties, Shigeru Iitaka
  77. Lectures on the Theory of Algebraic Numbers, E. T. Hecke
  78. A Course in Universal Algebra, Burris, Stanley and Sankappanavar, H. P.
  79. An Introduction to Ergodic Theory, Peter Walters
  80. A Course in the Theory of Groups,
  81. Lectures on Riemann Surfaces,
  82. Differential Forms in Algebraic Topology, Raoul Bott, Loring W. Tu
  83. Introduction to Cyclotomic Fields, Lawrence C. Washington
  84. A Classical Introduction to Modern Number Theory, Kenneth Ireland, Michael Rosen
  85. Fourier Series - A Modern Introduction Volume 2, R. E. Edwards
  86. Introduction to Coding Theory, J. H. van Lint
  87. Cohomology of Groups, Kenneth S. Brown
  88. Associative Algebras, R. S. Pierce
  89. Introduction to Algebraic and Abelian Functions, Serge Lang
  90. An Introduction to Convex Polytopes, Arne Brondsted
  91. The Geometry of Discrete Groups,
  92. Sequences and Series in Banach Spaces, J. Diestel
  93. Modern Geometry — Methods and Applications Part I: The Geometry of Surfaces, Transformation Groups, and Fields, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov
  94. Foundations of Differentiable Manifolds and Lie Groups,
  95. Probability-1, Probability-2, Albert N. Shiryaev
  96. A Course in Functional Analysis, John B. Conway
  97. Introduction to Elliptic Curves and Modular Forms, Neal I. Koblitz
  98. Representations of Compact Lie Groups,, Tammo tom Dieck
  99. Finite Reflection Groups, L.C. Grove, C.T. Benson
  100. Harmonic Analysis on Semigroups - Theory of Positive Definite and Related Functions, Christian Berg, Jens Peter Reus Christensen, Paul Ressel
  101. Galois Theory, Harold M. Edwards
  102. Lie Groups, Lie Algebras, and Their Representations, V. S. Varadarajan
  103. Complex Analysis, Serge Lang
  104. Modern Geometry — Methods and Applications Part II: The Geometry and Topology of Manifolds, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov
  105. SL2, Serge Lang
  106. The Arithmetic of Elliptic Curves, Joseph H. Silverman
  107. Applications of Lie Groups to Differential Equations, Peter J. Olver
  108. Holomorphic Functions and Integral Representations in Several Complex Variables, R. Michael Range
  109. Univalent Functions and Teichmüller Spaces, O. Lehto
  110. Algebraic Number Theory, Serge Lang
  111. Elliptic Curves,
  112. Elliptic Functions, Serge Lang
  113. Brownian Motion and Stochastic Calculus, Ioannis Karatzas, Steven Shreve
  114. A Course in Number Theory and Cryptography, Neal Koblitz
  115. Differential Geometry: Manifolds, Curves and Surfaces, Marcel Berger, Bernard Gostiaux
  116. Measure and Integral — Volume 1, John L. Kelley, T.P. Srinivasan
  117. Algebraic Groups and Class Fields, Jean-Pierre Serre
  118. Analysis Now, Gert K. Pedersen
  119. An Introduction to Algebraic Topology, Joseph J. Rotman,
  120. Weakly Differentiable Functions — Sobolev Spaces and Functions of Bounded Variation, William P. Ziemer
  121. Cyclotomic Fields I and II, Serge Lang
  122. Theory of Complex Functions, Reinhold Remmert
  123. Numbers, Heinz-Dieter Ebbinghaus et al.
  124. Modern Geometry — Methods and Applications Part III: Introduction to Homology Theory, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov
  125. Complex Variables — An Introduction, Carlos A. Berenstein, Roger Gay
  126. Linear Algebraic Groups, Armand Borel
  127. A Basic Course in Algebraic Topology, William S. Massey
  128. Partial Differential Equations, Jeffrey Rauch
  129. Representation Theory, William Fulton, Joe Harris
  130. Tensor Geometry — The Geometric Viewpoint and its Uses, Christopher T. J. Dodson, Timothy Poston
  131. A First Course in Noncommutative Rings, T. Y. Lam
  132. Iteration of Rational Functions — Complex Analytic Dynamical Systems, Alan F. Beardon
  133. Algebraic Geometry, Joe Harris
  134. Coding and Information Theory, Steven Roman
  135. Advanced Linear Algebra, Steven Roman
  136. Algebra — An Approach via Module Theory, William Adkins, Steven Weintraub
  137. Harmonic Function Theory, Sheldon Axler, Paul Bourdon, Wade Ramey
  138. A Course in Computational Algebraic Number Theory, Henri Cohen
  139. Topology and Geometry, Glen E. Bredon
  140. Optima and Equilibria, Jean-Pierre Aubin
  141. Gröbner Bases — A Computational Approach to Commutative Algebra, Thomas Becker, Volker Weispfenning
  142. Real and Functional Analysis, Serge Lang
  143. Measure Theory, J. L. Doob
  144. Noncommutative Algebra, Benson Farb, R. Keith Dennis
  145. Homology Theory — An Introduction to Algebraic Topology, James W. Vick
  146. Computability — A Mathematical Sketchbook, Douglas S. Bridges
  147. Algebraic K-Theory and Its Applications, Jonathan Rosenberg
  148. An Introduction to the Theory of Groups, Joseph J. Rotman
  149. Foundations of Hyperbolic Manifolds, John G. Ratcliffe
  150. Commutative Algebra — with a View Toward Algebraic Geometry, David Eisenbud
  151. Advanced Topics in the Arithmetic of Elliptic Curves, Joseph H. Silverman
  152. Lectures on Polytopes, Günter M. Ziegler
  153. Algebraic Topology — A First Course, William Fulton
  154. An Introduction to Analysis, Arlen Brown, Carl Pearcy
  155. Quantum Groups, Christian Kassel
  156. Classical Descriptive Set Theory, Alexander S. Kechris
  157. Integration and Probability, Paul Malliavin
  158. Field Theory, Steven Roman
  159. Functions of One Complex Variable II, John B. Conway
  160. Differential and Riemannian Manifolds, Serge Lang
  161. Polynomials and Polynomial Inequalities, Peter Borwein, Tamas Erdelyi
  162. Groups and Representations, J. L. Alperin, Rowen B. Bell
  163. Permutation Groups, John D. Dixon, Brian Mortimer
  164. Additive Number Theory The Classical Bases, Melvyn B. Nathanson
  165. Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Melvyn B. Nathanson
  166. Differential Geometry — Cartan's Generalization of Klein's Erlangen Program, R. W. Sharpe
  167. Field and Galois Theory, Patrick Morandi
  168. Combinatorial Convexity and Algebraic Geometry, Guenter Ewald
  169. Matrix Analysis, Rajendra Bhatia
  170. Sheaf Theory, Glen E. Bredon
  171. Riemannian Geometry, Peter Petersen
  172. Classical Topics in Complex Function Theory, Reinhold Remmert
  173. Graph Theory,
  174. Foundations of Real and Abstract Analysis, Douglas S. Bridges
  175. An Introduction to Knot Theory, W. B. Raymond Lickorish
  176. Introduction to Riemannian Manifolds, John M. Lee
  177. Analytic Number Theory , Donald J. Newman
  178. Nonsmooth Analysis and Control Theory, Francis H. Clarke, Yuri S. Ledyaev, Ronald J. Stern, Peter R. Wolenski
  179. Banach Algebra Techniques in Operator Theory, Ronald G. Douglas
  180. A Course on Borel Sets, S. M. Srivastava
  181. Numerical Analysis, Rainer Kress
  182. Ordinary Differential Equations, Wolfgang Walter
  183. An Introduction to Banach Space Theory, Robert E. Megginson
  184. Modern Graph Theory, Béla Bollobás
  185. Using Algebraic Geometry, David A. Cox, John Little, Donal O'Shea
  186. Fourier Analysis on Number Fields, Dinakar Ramakrishnan, Robert J. Valenza
  187. Moduli of Curves, Joe Harris, Ian Morrison
  188. Lectures on the Hyperreals, Robert Goldblatt
  189. Lectures on Modules and Rings, Tsit-Yuen Lam
  190. Problems in Algebraic Number Theory, M. Ram Murty, Jody Indigo Esmonde
  191. Fundamentals of Differential Geometry, Serge Lang
  192. Elements of Functional Analysis, Francis Hirsch, Gilles Lacombe
  193. Advanced Topics in Computational Number Theory, Henri Cohen
  194. One-Parameter Semigroups for Linear Evolution Equations, Engel, Nagel
  195. Elementary Methods in Number Theory, Melvyn B. Nathanson
  196. Basic Homological Algebra, M. Scott Osborne
  197. The Geometry of Schemes, Eisenbud, Joe Harris
  198. A Course in p-adic Analysis, Alain M. Robert
  199. Theory of Bergman Spaces, Hakan Hedenmalm, Boris Korenblum, Kehe Zhu
  200. An Introduction to Riemann-Finsler Geometry, David Bao, Shiing-Shen Chern, Zhongmin Shen
  201. Diophantine Geometry, Marc Hindry, Joseph H. Silverman
  202. Introduction to Topological Manifolds, John M. Lee
  203. The Symmetric Group — Representations, Combinatorial Algorithms, and Symmetric Functions, Bruce E. Sagan
  204. Galois Theory, Jean-Pierre Escofier
  205. Rational Homotopy Theory, Yves Félix, Stephen Halperin, Jean-Claude Thomas
  206. Problems in Analytic Number Theory, M. Ram Murty
  207. Algebraic Graph Theory, Chris Godsil, Gordon Royle
  208. Analysis for Applied Mathematics, Ward Cheney
  209. A Short Course on Spectral Theory, William Arveson
  210. Number Theory in Function Fields, Michael Rosen
  211. Algebra, Serge Lang
  212. Lectures on Discrete Geometry, Jiří Matoušek
  213. From Holomorphic Functions to Complex Manifolds,, Hans Grauert
  214. Partial Differential Equations, Jürgen Jost,
  215. Algebraic Functions and Projective Curves, David M. Goldschmidt,
  216. Matrices — Theory and Applications, Denis Serre,
  217. Model Theory: An Introduction, David Marker,
  218. Introduction to Smooth Manifolds, John M. Lee
  219. The Arithmetic of Hyperbolic 3-Manifolds, Colin Maclachlan, Alan W. Reid,
  220. Smooth Manifolds and Observables, Jet Nestruev,
  221. Convex Polytopes, Branko Grünbaum
  222. Lie Groups, Lie Algebras, and Representations - An Elementary Introduction, Brian C. Hall,
  223. Fourier Analysis and its Applications, Anders Vretblad,
  224. Metric Structures in Differential Geometry, Walschap, G.,
  225. Lie Groups, Daniel Bump,
  226. Spaces of Holomorphic Functions in the Unit Ball, Kehe Zhu,
  227. Combinatorial Commutative Algebra, Ezra Miller, Bernd Sturmfels,
  228. A First Course in Modular Forms, Fred Diamond, J. Shurman,
  229. The Geometry of Syzygies, David Eisenbud
  230. An Introduction to Markov Processes, Daniel W. Stroock,
  231. Combinatorics of Coxeter Groups, Anders Björner, Francisco Brenti,
  232. An Introduction to Number Theory, Everest, Graham., Ward, T.,
  233. Topics in Banach Space Theory, Albiac, F., Kalton, N. J.,
  234. Analysis and Probability — Wavelets, Signals, Fractals, Jorgensen, P. E. T.,
  235. Compact Lie Groups, M. R. Sepanski,
  236. Bounded Analytic Functions, Garnett, J.,
  237. An Introduction to Operators on the Hardy-Hilbert Space, Ruben A. Martinez-Avendano, Peter Rosenthal,
  238. A Course in Enumeration, Aigner, M.,
  239. Number Theory — Volume I: Tools and Diophantine Equations, Cohen, H.,
  240. Number Theory — Volume II: Analytic and Modern Tools, Cohen, H.,
  241. The Arithmetic of Dynamical Systems, Joseph H. Silverman,
  242. Abstract Algebra, Grillet, Pierre Antoine,
  243. Topological Methods in Group Theory, Geoghegan, Ross,
  244. Graph Theory, Adrian Bondy, U.S.R. Murty,
  245. Complex Analysis: Introduced in the Spirit of Lipman Bers, Gilman, Jane P., Kra, Irwin, Rodríguez, Rubí E.
  246. A Course in Commutative Banach Algebras, Kaniuth, Eberhard,
  247. Braid Groups, Kassel, Christian, Turaev, Vladimir,
  248. Buildings Theory and Applications, Abramenko, Peter, Brown, Ken
  249. Classical Fourier Analysis, Loukas Grafakos
  250. Modern Fourier Analysis, Loukas Grafakos
  251. The Finite Simple Groups, Robert A. Wilson
  252. Distributions and Operators, Gerd Grubb,
  253. Elementary Functional Analysis, MacCluer, Barbara D.,
  254. Algebraic Function Fields and Codes,,
  255. Symmetry, Representations, and Invariants, Goodman, Roe, Wallach, Nolan R.,
  256. A Course in Commutative Algebra, Kemper, Gregor,
  257. Deformation Theory, Robin Hartshorne,
  258. Foundations of Optimization in Finite Dimensions, Osman Guler,
  259. Ergodic Theory - with a view towards Number Theory, Thomas Ward, Manfred Einsiedler,
  260. Monomial Ideals, Jürgen Herzog, Hibi Takayuki
  261. Probability and Stochastics, Erhan Cinlar,
  262. Essentials of Integration Theory for Analysis, Daniel W. Stroock,
  263. Analysis on Fock Spaces, Kehe Zhu,
  264. Functional Analysis, Calculus of Variations and Optimal Control, Francis H. Clarke,
  265. Unbounded Self-adjoint Operators on Hilbert Space, Konrad Schmüdgen,
  266. Calculus Without Derivatives, Jean-Paul Penot,
  267. Quantum Theory for Mathematicians, Brian C. Hall,
  268. Geometric Analysis of the Bergman Kernel and Metric, Krantz, Steven G.,
  269. Locally Convex Spaces, M Scott Osborne,
  270. Fundamentals of Algebraic Topology, Steven Weintraub,
  271. Integer Programming, Michelangelo Conforti, Gérard P. Cornuéjols, Giacomo Zambelli,
  272. Operator Theoretic Aspects of Ergodic Theory, Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel,
  273. Homotopical Topology, Anatoly Fomenko, Dmitry Fuchs,
  274. Brownian Motion, Martingales, and Stochastic Calculus, Jean-François Le Gall,
  275. Differential Geometry - Connections, Curvature, and Characteristic Classes, Loring W. Tu
  276. Functional Analysis, Spectral Theory, and Applications, Manfred Einsiedler, Thomas Ward
  277. The Moment Problem, Konrad Schmüdgen
  278. Modern Real Analysis, William P. Ziemer
  279. Binomial Ideals, Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi
  280. Introduction to Real Analysis, Christopher Heil
  281. Intersection Homology & Perverse Sheaves with Applications to Singularities, Laurenţiu G. Maxim
  282. Measure, Integration & Real Analysis, Sheldon Axler
  283. Basic Representation Theory of Algebras, Ibrahim Assem, Flávio U Coelho
  284. Spectral Theory, David Borthwick
  285. An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space, Konrad Schmüdgen
  286. Lectures on Convex Geometry, Daniel Hug, Wolfgang Weilt
  287. Explorations in Complex Functions, Richard Beals, Roderick S. C. Wong
  288. Quaternion Algebras, John Voight