Graduate Studies in Mathematics

Graduate Studies in Mathematics is a series of graduate-level textbooks in mathematics published by the American Mathematical Society. The books in this series are published in hardcover and e-book formats.

List of books

Volume	Title	Author	Year	ISBN
1	The General Topology of Dynamical Systems	Ethan Akin	1993
2	Combinatorial Rigidity	Jack Graver, Brigitte Servatius, Herman Servatius	1993
3	An Introduction to Gröbner Bases	William W. Adams, Philippe Loustaunau	1994
4	The Integrals of Lebesgue, Denjoy, Perron, and Henstock	Russell A. Gordon	1994
5	Algebraic Curves and Riemann Surfaces	Rick Miranda	1995
6	Lectures on Quantum Groups	Jens Carsten Jantzen	1996
7	Algebraic Number Fields	Gerald J. Janusz	1996, 2nd ed.
8	Discovering Modern Set Theory. I: The Basics	Winfried Just, Martin Weese	1996
9	An Invitation to Arithmetic Geometry	Dino Lorenzini	1996
10	Representations of Finite and Compact Groups	Barry Simon	1996
11	Enveloping Algebras	Jacques Dixmier	1996
12	Lectures on Elliptic and Parabolic Equations in Hölder Spaces	N. V. Krylov	1996
13	The Ergodic Theory of Discrete Sample Paths	Paul C. Shields	1996
14	Analysis	Elliott H. Lieb, Michael Loss	2001, 2nd ed.
15	Fundamentals of the Theory of Operator Algebras. Volume I: Elementary Theory	Richard V. Kadison, John R. Ringrose	1997
16	Fundamentals of the Theory of Operator Algebras. Volume II: Advanced Theory	Richard V. Kadison, John R. Ringrose	1997
17	Topics in Classical Automorphic Forms	Henryk Iwaniec	1997
18	Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician	Winfried Just, Martin Weese	1997
19	Partial Differential Equations	Lawrence C. Evans	2010, 2nd ed.
20	4-Manifolds and Kirby Calculus	Robert E. Gompf, András I. Stipsicz	1999
21	A Course in Operator Theory	John B. Conway	2000
22	Growth of Algebras and Gelfand-Kirillov Dimension	Günter R. Krause, Thomas H. Lenagan	2000, Revised ed.
23	Foliations I	Alberto Candel, Lawrence Conlon	2000
24	Number Theory: Algebraic Numbers and Functions	Helmut Koch	2000
25	Dirac Operators in Riemannian Geometry	Thomas Friedrich	2000
26	An Introduction to Symplectic Geometry	Rolf Berndt	2001
27	A Course in Differential Geometry	Thierry Aubin	2001
28	Notes on Seiberg-Witten Theory	Liviu I. Nicolaescu	2000
29	Fourier Analysis	Javier Duoandikoetxea	2001
30	Noncommutative Noetherian Rings	J. C. McConnell, J. C. Robson	1987
31	Option Pricing and Portfolio Optimization: Modern Methods of Financial Mathematics	Ralf Korn, Elke Korn	2001
32	A Modern Theory of Integration	Robert G. Bartle	2001
33	A Course in Metric Geometry	Dmitri Burago, Yuri Burago, Sergei Ivanov	2001
34	Differential Geometry, Lie Groups, and Symmetric Spaces	Sigurdur Helgason	2001
35	Lecture Notes in Algebraic Topology	James F. Davis, Paul Kirk	2001
36	Principles of Functional Analysis	Martin Schechter	2002, 2nd ed.
37	Theta Constants, Riemann Surfaces and the Modular Group: An Introduction with Applications to Uniformization Theorems, Partition Identities and Combinatorial Number Theory	Hershel M. Farkas, Irwin Kra	2001
38	Stochastic Analysis on Manifolds	Elton P. Hsu	2002
39	Classical Groups and Geometric Algebra	Larry C. Grove	2002
40	Function Theory of One Complex Variable	Robert E. Greene, Steven G. Krantz	2006, 3rd ed.
41	Introduction to the Theory of Differential Inclusions	Georgi V. Smirnov	2002
42	Introduction to Quantum Groups and Crystal Bases	Jin Hong, Seok-Jin Kang	2002
43	Introduction to the Theory of Random Processes	N. V. Krylov	2002
44	Pick Interpolation and Hilbert Function Spaces	Jim Agler, John E. McCarthy	2002
45	An Introduction to Measure and Integration	Inder K. Rana	2002, 2nd ed.
46	Several Complex Variables with Connections to Algebraic Geometry and Lie Groups	Joseph L. Taylor	2002
47	Classical and Quantum Computation	A. Yu. Kitaev, A. H. Shen, M. N. Vyalyi	2002
48	Introduction to the h-Principle	Y. Eliashberg, N. Mishachev	2002
49	Secondary Cohomology Operations	John R. Harper	2002
50	An Invitation to Operator Theory	Y. A. Abramovich, C. D. Aliprantis	2002
51	Problems in Operator Theory	Y. A. Abramovich, C. D. Aliprantis	2002
52	Global Analysis: Differential Forms in Analysis, Geometry and Physics	Ilka Agricola, Thomas Friedrich	2002
53	Spectral Methods of Automorphic Forms	Henryk Iwaniec	2002, 2nd ed.
54	A Course in Convexity	Alexander Barvinok	2002
55	A Scrapbook of Complex Curve Theory	C. Herbert Clemens	2003, 2nd ed.
56	A Course in Algebra	E. B. Vinberg	2003
57	Concise Numerical Mathematics	Robert Plato	2003
58	Topics in Optimal Transportation	Cédric Villani	2003
59	Representation Theory of Finite Groups: Algebra and Arithmetic	Steven H. Weintraub	2003
60	Foliations II	Alberto Candel, Lawrence Conlon	2003
61	Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems	Thomas A. Ivey, J. M. Landsberg	2003
62	A Companion to Analysis: A Second First and First Second Course in Analysis	T. W. Körner	2004
63	Resolution of Singularities	Steven Dale Cutkosky	2004
64	Lectures on the Orbit Method	A. A. Kirillov	2004
65	Global Calculus	S. Ramanan	2005
66	Functional Analysis: An Introduction	Yuli Eidelman, Vitali Milman, Antonis Tsolomitis	2004
67	Introduction to Quadratic Forms over Fields	T.Y. Lam	2005
68	A Geometric Approach to Free Boundary Problems	Luis Caffarelli, Sandro Salsa	2005
69	Curves and Surfaces	Sebastián Montiel, Antonio Ros	2009, 2nd ed.
70	Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula	Seán Dineen	2013, 2nd ed.
71	Modern Geometric Structures and Fields	S. P. Novikov, I. A. Taimanov	2006
72	Introduction to the Mathematics of Finance	Ruth J. Williams	2006
73	Graduate Algebra: Commutative View	Louis Halle Rowen	2006
74	Elements of Combinatorial and Differential Topology	V. V. Prasolov	2006
75	Applied Asymptotic Analysis	Peter D. Miller	2006
76	Measure Theory and Integration	Michael E. Taylor	2006
77	Hamilton's Ricci Flow	Bennett Chow, Peng Lu, Lei Ni	2006
78	Linear Algebra in Action	Harry Dym	2013, 2nd ed.
79	Modular Forms, a Computational Approach	William A. Stein	2007
80	Probability	Davar Khoshnevisan	2007
81	Elements of Homology Theory	V. V. Prasolov	2007
82	Pseudo-differential Operators and the Nash-Moser Theorem	Serge Alinhac, Patrick Gérard	2007
83	Functions of Several Complex Variables and Their Singularities	Wolfgang Ebeling	2007
84	Cones and Duality	Charalambos D. Aliprantis, Rabee Tourky	2007
85	Recurrence and Topology	John M. Alongi, Gail S. Nelson	2007
86	Lectures on Analytic Differential Equations	Yulij Ilyashenko, Sergei Yakovenko	2008
87	Twenty-Four Hours of Local Cohomology	Srikanth B. Iyengar, Graham J. Leuschke, Anton Leykin, Claudia Miller, Ezra Miller, Anurag K. Singh, Uli Walther	2007
88	C∗-Algebras and Finite-Dimensional Approximations	Nathanial P. Brown, Narutaka Ozawa	2008
89	A Course on the Web Graph	Anthony Bonato	2008
90	Basic Quadratic Forms	Larry J. Gerstein	2008
91	Graduate Algebra: Noncommutative View	Louis Halle Rowen	2008
92	Finite Group Theory	I. Martin Isaacs	2008
93	Topics in Differential Geometry	Peter W. Michor	2008
94	Representations of Semisimple Lie Algebras in the BGG Category O	James E. Humphreys	2008
95	Quantum Mechanics for Mathematicians	Leon A. Takhtajan	2008
96	Lectures on Elliptic and Parabolic Equations in Sobolev Spaces	N. V. Krylov	2008
97	Complex Made Simple	David C. Ullrich	2008
98	Discrete Differential Geometry: Integrable Structure	Alexander I. Bobenko, Yuri B. Suris	2008
99	Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators	Gerald Teschl	2009
100	Algebra: A Graduate Course	I. Martin Isaacs	1994
101	A Course in Approximation Theory	Ward Cheney, Will Light	2000
102	Introduction to Fourier Analysis and Wavelets	Mark A. Pinsky	2002
103	Configurations of Points and Lines	Branko Grünbaum	2009
104	Algebra: Chapter 0	Paolo Aluffi	2009
105	A First Course in Sobolev Spaces	Giovanni Leoni	2009
106	Embeddings in Manifolds	Robert J. Daverman, Gerard A. Venema	2009
107	Manifolds and Differential Geometry	Jeffrey M. Lee	2009
108	Mapping Degree Theory	Enrique Outerelo, Jesús M. Ruiz	2009
109	Training Manual on Transport and Fluids	John C. Neu	2010
110	Differential Algebraic Topology: From Stratifolds to Exotic Spheres	Matthias Kreck	2010
111	Ricci Flow and the Sphere Theorem	Simon Brendle	2010
112	Optimal Control of Partial Differential Equations: Theory, Methods and Applications	Fredi Troltzsch	2010
113	Continuous Time Markov Processes: An Introduction	Thomas M. Liggett	2010
114	Advanced Modern Algebra	Joseph J. Rotman	2010, 2nd ed.
115	An Introductory Course on Mathematical Game Theory	Julio González-Díaz, Ignacio García-Jurado, M. Gloria Fiestras-Janeiro	2010
116	Linear Functional Analysis	Joan Cerdà	2010
117	An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog	Terence Tao	2010
118	Dynamical Systems and Population Persistence	Hal L. Smith, Horst R. Thieme	2011
119	Mathematical Statistics: Asymptotic Minimax Theory	Alexander Korostelev, Olga Korosteleva	2011
120	A Basic Course in Partial Differential Equations	Qing Han	2011
121	A Course in Minimal Surfaces	Tobias Holck Colding, William P. Minicozzi II	2011
122	Algebraic Groups and Differential Galois Theory	Teresa Crespo, Zbigniew Hajto	2011
123	Lectures on Linear Partial Differential Equations	Gregory Eskin	2011
124	Toric Varieties	David A. Cox, John B. Little, Henry K. Schenck	2011
125	Riemann Surfaces by Way of Complex Analytic Geometry	Dror Varolin	2011
126	An Introduction to Measure Theory	Terence Tao	2011
127	Modern Classical Homotopy Theory	Jeffrey Strom	2011
128	Tensors: Geometry and Applications	J. M. Landsberg	2012
129	Classical Methods in Ordinary Differential Equations: With Applications to Boundary Value Problems	Stuart P. Hastings, J. Bryce McLeod	2012
130	Gröbner Bases in Commutative Algebra	Viviana Ene, Jürgen Herzog	2011
131	Lie Superalgebras and Enveloping Algebras	Ian M. Musson	2012
132	Topics in Random Matrix Theory	Terence Tao	2012
133	Hyperbolic Partial Differential Equations and Geometric Optics	Jeffrey Rauch	2012
134	Analytic Number Theory: Exploring the Anatomy of Integers	Jean-Marie De Koninck, Florian Luca	2012
135	Linear and Quasi-linear Evolution Equations in Hilbert Spaces	Pascal Cherrier, Albert Milani	2012
136	Regularity of Free Boundaries in Obstacle-Type Problems	Arshak Petrosyan, Henrik Shahgholian, Nina Uraltseva	2012
137	Ordinary Differential Equations: Qualitative Theory	Luis Barreira, Clàudia Valls	2012
138	Semiclassical Analysis	Maciej Zworski	2012
139	Knowing the Odds: An Introduction to Probability	John B. Walsh	2012
140	Ordinary Differential Equations and Dynamical Systems	Gerald Teschl	2012
141	A Course in Abstract Analysis	John B. Conway	2012
142	Higher Order Fourier Analysis	Terence Tao	2012
143	Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations	Alberto Bressan	2013
144	Dualities and Representations of Lie Superalgebras	Shun-Jen Cheng, Weiqiang Wang	2012
145	The K-book: An Introduction to Algebraic K-theory	Charles A. Weibel	2013
146	Combinatorial Game Theory	Aaron N. Siegel	2013
147	Matrix Theory	Xingzhi Zhan	2013
148	Introduction to Smooth Ergodic Theory	Luis Barreira, Yakov Pesin	2013
149	Mathematics of Probability	Daniel W. Stroock	2013
150	The Joys of Haar Measure	Joe Diestel, Angela Spalsbury	2013
151	Introduction to 3-Manifolds	Jennifer Schultens	2014
152	An Introduction to Extremal Kähler Metrics	Gábor Székelyhidi	2014
153	Hilbert's Fifth Problem and Related Topics	Terence Tao	2014
154	A Course in Complex Analysis and Riemann Surfaces	Wilhelm Schlag	2014
155	An Introduction to the Representation Theory of Groups	Emmanuel Kowalski	2014
156	Functional Analysis: An Elementary Introduction	Markus Haase	2014
157	Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators	Gerald Teschl	2014, 2nd ed.
158	Dynamical Systems and Linear Algebra	Fritz Colonius, Wolfgang Kliemann	2014
159	The Role of Nonassociative Algebra in Projective Geometry	John R. Faulkner	2014
160	A Course in Analytic Number Theory	Marius Overholt	2014
161	Introduction to Tropical Geometry	Diane Maclagan, Bernd Sturmfels	2015
162	A Course on Large Deviations with an Introduction to Gibbs Measures	Firas Rassoul-Agha, Timo Seppäläinen	2015
163	Introduction to Analytic and Probabilistic Number Theory	Gérald Tenenbaum	2015, 3rd ed.
164	Expansion in Finite Simple Groups of Lie Type	Terence Tao	2015
165	Advanced Modern Algebra, Part 1	Joseph J. Rotman	2015, 3rd ed.
166	Problems in Real and Functional Analysis	Alberto Torchinsky	2015
167	Singular Perturbation in the Physical Sciences	John C. Neu	2015
168	Random Operators: Disorder Effects on Quantum Spectra and Dynamics	Michael Aizenman, Simone Warzel	2015
169	Partial Differential Equations: An Accessible Route through Theory and Applications	András Vasy	2015
170	Colored Operads	Donald Yau	2016
171	Nonlinear Elliptic Equations of the Second Order	Qing Han	2016
172	Combinatorics and Random Matrix Theory	Jinho Baik, Percy Deift, Toufic Suidan	2016
173	Differentiable Dynamical Systems: An Introduction to Structural Stability and Hyperbolicity	Lan Wen	2016
174	Quiver Representations and Quiver Varieties	Alexander Kirillov Jr.	2016
175	Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems	Thomas A. Ivey, Joseph M. Landsberg	2016, 2nd ed.
176	Ordered Groups and Topology	Adam Clay, Dale Rolfsen	2016
177	Differential Galois Theory through Riemann–Hilbert Correspondence: An Elementary Introduction	Jacques Sauloy	2016
178	From Frenet to Cartan: The Method of Moving Frames	Jeanne N. Clelland	2017
179	Modular Forms: A Classical Approach	Henri Cohen, Fredrik Strömberg	2017
180	Advanced Modern Algebra, Part 2	Joseph J. Rotman	2017, 3rd ed.
181	A First Course in Sobolev Spaces	Giovanni Leoni	2017, 2nd ed.
182	Nonlinear PDEs: A Dynamical Systems Approach	Guido Schneider, Hannes Uecker	2017
183	Separable Algebras	Timothy J. Ford	2017
184	An Introduction to Quiver Representations	Harm Derksen, Jerzy Weyman	2017
185	Braid Foliations in Low-Dimensional Topology	Douglas J. LaFountain, William W. Menasco	2017
186	Rational Points on Varieties	Bjorn Poonen	2017
187	Introduction to Global Analysis: Minimal Surfaces in Riemannian Manifolds	John Douglas Moore	2017
188	Introduction to Algebraic Geometry	Steven Dale Cutkosky	2018
189	Characters of Solvable Groups	I. Martin Isaacs	2018
190	Lectures on Finite Fields	Xiang-dong Hou	2018
191	Functional Analysis	Theo Bühler, Dietmar A. Salamon	2018
192	Lectures on Navier-Stokes Equations	Tai-Peng Tsai	2018
193	A Tour of Representation Theory	Martin Lorenz	2018
194	Algebraic Statistics	Seth Sullivant	2018
195	Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics	Matthias Beck, Raman Sanyal	2018
196	Convection-Diffusion Problems: An Introduction to Their Analysis and Numerical Solution	Martin Stynes, David Stynes	2018
197	A Course on Partial Differential Equations	Walter Craig	2018
198	Dynamics in One Non-Archimedean Variable	Robert L Benedetto	2019
199	Applied Stochastic Analysis	Weinan E, Tiejun Li, Eric Vanden-Eijnden	2019
200	Mathematical Theory of Scattering Resonances	Semyon Dyatlov, Maciej Zworski	2019
201	Geometric Relativity	Dan A Lee	2019
202	Introduction to Complex Analysis	Michael E Taylor	2019
203	The Distribution of Prime Numbers	Dimitris Koukoulopoulos	2019
204	Hochschild Cohomology for Algebras	Sarah J. Witherspoon	2019
205	Invitation to Partial Differential Equations	Maxim Braverman, Robert McOwen, Peter Topalov, Mikhail Shubin	2020
206	Extrinsic Geometric Flows	Ben Andrews, Bennett Chow, Christine Guenther, Mat Langford	2020
207	Organized Collapse: An Introduction to Discrete Morse Theory	Dmitry N. Kozlov	2020
208	Geometry and Topology of Manifolds: Surfaces and Beyond	Vicente Muñoz, Ángel González-Prieto, Juan Ángel Rojo	2020
209	Hyperbolic Knot Theory	Jessica Purcell	2020
210	Combinatorics: The Art of Counting	Bruce E. Sagan	2020
211	Invitation to Nonlinear Algebra	, Bernd Sturmfels	2021
212	Differential Equations: A Dynamical Systems Approach to Theory and Practice	Marcelo Viana, José M. Espinar	2021
213	Hamilton–Jacobi Equations: Theory and Applications	Hung Vinh Tran	2021
214	Portfolio Theory and Arbitrage: A Course in Mathematical Finance	Ioannis Karatzas, Constantinos Kardaras	2021
215	Shock Waves	Tai-Ping Liu	2021
216	A Concise Introduction to Algebraic Varieties	Brian Osserman	2021
217	Lectures on Poisson Geometry	Marius Crainic, Rui Loja Fernandes, Ioan Mărcuț	2021
218	Lectures on Differential Topology	Riccardo Benedetti	2021
219	Essentials of Tropical Combinatorics	Michael Joswig	2021
220	Ultrafilters Throughout Mathematics	Isaac Goldbring	2022
221	One-Dimensional Ergodic Schrödinger Operators: I. General Theory	David Damanik, Jake Fillman	2022
222	Algebraic Geometry: Notes on a Course	Michael Artin	2022
223	Groups and Topological Dynamics	Volodymyr Nekrashevych	2022
224	Discrete Analogues in Harmonic Analysis: Bourgain, Stein, and Beyond	Ben Krause	2022
225	The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction	Jacob Bedrossian, Vlad Vicol	2022
226	A First Course in Spectral Theory	Milivoje Lukić	2022
227	Geometric Structures on Manifolds	William M. Goldman	2022
228	Topological and Ergodic Theory of Symbolic Dynamics	Henk Bruin	2022
229	A First Course in Fractional Sobolev Spaces	Giovanni Leoni	2023
230	Inverse Problems for Fractional Partial Differential Equations	Barbara Kaltenbacher, William Rundell	2023
231	Introduction to Smooth Ergodic Theory	Luis Barreira, Yakov Pesin	2023, 2nd ed.
232	Linear Algebra in Action	Harry Dym	2023, 3rd ed.
233	Commutative Algebra	Andrea Ferretti	2023
234	Homological Methods in Commutative Algebra	Andrea Ferretti	2023
235	Ricci Solitons in Low Dimensions	Bennett Chow	2023
236	Alexandrov Geometry: Foundations	Stephanie Alexander, Vitali Kapovitch, Anton Petrunin	2024
237	Topics in Spectral Geometry	Michael Levitin, Dan Mangoubi, Iosif Polterovich	2023
238	An Introductory Course on Mathematical Game Theory	Julio González-Díaz, Ignacio García-Jurado, M. Gloria Fiestras-Janeiro	2023, 2nd ed.
239	Introduction to the h-Principle	K. Cieliebak, Y. Eliashberg, N. Mishachev	2024, 2nd ed.
240	Analysis of Monge–Ampère Equations	Nam Q. Le	2024
241	Real Algebraic Geometry and Optimization	Thorsten Theobald	2024
242	Translation Surfaces	Jayadev S. Athreya, Howard Masur	2024
243	Quantum Computation and Quantum Information: A Mathematical Perspective	J. M. Landsberg	2024
244	Introduction to Complex Manifolds	John M. Lee	2024
245	Lectures on Differential Geometry	Bennett Chow, Yutze Chow	2024
246	Bifurcation Theory	Ale Jan Homburg, Jürgen Knobloch	2024
247	An Invitation to Fractal Geometry: Fractal Dimensions, Self-Similarity, and Fractal Curves	Michel L. Lapidus, Goran Radunović	2024
248	Introduction to Lie Algebras: Finite and Infinite Dimension	J. I. Hall	2024
249	One-Dimensional Ergodic Schrödinger Operators: II. Specific Classes	David Damanik, Jake Fillman	2024
250	The Practice of Algebraic Curves: A Second Course in Algebraic Geometry	David Eisenbud, Joe Harris	2024
251	Inequalities in Matrix Algebras	Eric Carlen	2025