Algebraic Number Theory

Analytic Number Theory

Class Field Theory

Combinatorial Number Theory

Category Theory

Abstract Algebra

Complex Analysis

Real Analysis

Topology

Matroid Theory

Arithmetic Algebraic Geometry

Diophantine Geometry  (In progress)

Topoi Theory   (To Come)

Here is a compilation of pdfs that I have written, more precisely, I have taken multiple books in each field and have combined them each into a comprehensive study guide. Each pdf consists of the bulk/basics of each field, with proofs and examples being omitted. They are mostly complete, but will always be a work-in-progress. Whenever I commit to knowing/remembering something forever, I organize the material in such a way so that it is easy to engrain the information in my head… these books accomplish that.

I cannot proceed without giving credit to those authors whom I have learned most from, and whose material I have chosen to use in my references. They are: Tenenbaum, Montgomery, Vaughan, Apostle, Ireland, Rosen, Titchmarsh, Jarvis, Marcus, Alaca, Lang, Ash, Samuel, Neukirch, Tao, Vu, Nathanson, Ruzsa, Mac Lane, Leinster, Awodey, Hungerford, Dummit, Foote, Palka, Stein, Bass, Royden, Gordon, McNulty and Oxley.