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Book list:

Proofs:
-"How to Prove It", Velleman

Calculus:
-Stewart
-Spivak

Linear Algebra:
-"Linear Algebra Done Right"

Set Theory:
-"Naive Set Theory"

Abstract Algebra:
-"A Book of Abstract Algebra", Pinter
-Dummit & Foote
-"Algebra: Chapter 0"
-Artin
-Lang

Real Analysis:
-"Principles of Mathematical Analysis", Rudin
-"Understanding Analysis"

Complex Analysis:
-Stein & Shakarchi
-Ahlfors
-"Introductory Complex Analysis", Silverman
-"Real and Complex Analysis", Rudin

Topology:
-Munkres

Number Theory:
-"A Classical Introduction to Modern Number Theory"

Galois Theory:
-Artin
-Rotman

Commutative Algebra:
-"Introduction to Commutative Algebra", Atiyah & Macdonald
-"Commutative Rings", Kaplansky

Algebraic Topology:
-Hatcher

Differential Geometry:
-"Differential Geometry of Curves and Surfaces", Do Carmo

Elliptic Curves:
-"Arithmetic of Elliptic Curves", Silverman

Algebraic Geometry:
-"Ideals Varieties and Algorithms"
-"Algebraic Geometry: A Problem Solving Approach"

Harmonic Analysis:
-Stein & Murphy