Pure mathematics reference books.

1. "Principles of Mathematical Analysis" by Walter Rudin
2. "Introduction to Topology" by Bert Mendelson
3. "Linear Algebra" by Serge Lang
4. "Complex Analysis" by Joseph Bak and Donald J. Newman
5. "Number Theory" by George E. Andrews
6. "Differential Equations" by George F. Simmons
7. "Probability and Statistics" by Morris H. DeGroot and Mark J. Schervish
8. "Graph Theory" by Reinhard Diestel
9. "Combinatorics: Topics, Techniques, Algorithms" by Peter J. Cameron
10. "Algebraic Geometry" by Robin Hartshorne

Algebra

- Abstract Algebra by I. N. Herstein
- Algebra: Chapters 1-4 by N. Jacobson
- Galois Theory by I. Stewart
- Representation Theory of Finite Groups by B. Serre
- Algebraic Geometry by R. Hartshorne

Analysis

- Principles of Mathematical Analysis by W. Rudin
- Real Analysis by H. L. Royden
- Complex Analysis by J. Conway
- Measure Theory by P. Halmos
- Functional Analysis by W. Rudin

Topology

- Topology by J. R. Munkres
- Algebraic Topology by A. Hatcher
- Geometric Topology by R. Daverman
- Differential Topology by V. Guillemin and A. Pollack
- Symplectic Geometry by D. McDuff and D. Salamon

Number Theory

- Elementary Number Theory by D. M. Burton
- Number Theory by J. H. Silverman
- Algebraic Number Theory by J. Neukirch
- Analytic Number Theory by D. Hensley
- The Arithmetic of Elliptic Curves by J. Silverman

Logic

- Logic by M. Dummett
- Model Theory by W. Hodges
- Set Theory by K. Hrbacek and T. Jech
- Proof Theory by G. Gentzen
- Computability Theory by R. Soare

Combinatorics

- Combinatorics by C. A. Charalambides
- Graph Theory by D. B. West
- Enumeration in Combinatorics by C. Berge
- Matroid Theory by A. Björner, M. L. Las Vergnas, B. Sturmfels, N. White, and G. M. Ziegler
- Algebraic Combinatorics by R. P. Stanley

Other

- The Handbook of Mathematical Functions by M. Abramowitz and I. Stegun
- Mathematical Tables and Formulae by D. F. Harriman
- Mathematics for the Applied Sciences by J. Matthews
- Essential Mathematics for Scientists and Engineers by R. Cannon and P. C. Silva
- The Mathematical Experience by P. J. Davis and R. Hersh