I will include books and lecture notes in topics that I studied and that I feel fairly knowledgeable about.
Key
green = read and recommended by me
red = difficult to read
pink = elementary
grey = classic
blue = lecture notes
Real and Complex Analysis
Introductory
- Modern Real Analysis by William P. Ziemer
- Understanding Analysis by Stephen Abbott
- Principles of Mathematical Analysis by Walter Rudin
- Analysis Now by Gert K. Pedersen
Advanced
- Analysis, Sobolev Spaces and Partial Differential Equations by Gerald B. Folland
- Real and Complex Analysis by Walter Rudin
Functional Analysis
- Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis
- Functional Analysis by Walter Rudin
- Introductory Functional Analysis with Applications by Erwin Kreyszig
- Introduction to Topology and Modern Analysis by George F. Simmons
- History of Functional Analysis by Jean Dieudonné
- A course in Functional Analysis by John B. Conway
- Nonlinear Functional Analysis by Klaus Deimling
- Functional Analysis by Peter D. Lax
- Real and Functional Analysis by Serge Lang
Measure Theory
Introductory
- Measure Theory by by D.H.Fremlin
- Lebesgue Measure on Euclidean space by Frank Jone
- An introduction to measure theory by Terence Tao
Advanced
- Measure Theory Volume I by V.I. Bogachev
- Measure Theory Volume II by V.I. Bogachev
- Measure Theory by Paul R. Halmos
- Gaussian Measures by V.I. Bogachev
Stochastic Calculus
- Introduction to Stochastic Calculus with Applications by Fima C. Klebaner
- Stochastic Differential Equations by Bernt Oksendal
- A first Course in Stochastic Processes by Samuel Karlin and Howard M. Taylor
- Introduction to Probability Models by Sheldon M. Ross
- Brownian Motion - An Introduction to Stochastic Processes by René Schilling and Lothar Partzsch
Stochastic Calculus Applied to Finance
- Stochastic Calculus and Finance by Steven E. Shreve
- Stochastic Calculus and Financial Applications by Michael Steele
- Mathematical Finance by Ernst Eberlein and Jan Kallsen
- Interest Rate Models-Theory and Practice by Damiano Brigo and Fabio Mercurio
- The Volatility Surface-A Practitioner's Guide by Jim Gatheral
Finance
- Options, Futures and Other Derivatives by John C. Hull
- Commodities and Commodity Derivatives by Hélyette Geman
- Corporate Finance by Jonathan B. Berk and Peter DeMarzo
Quantum Mechanics
- Quantum Mechanics-A Paradigms Approach by David H. McIntyre
- Introduction to Quantum Mechanics by David J. Griffiths
- Lectures on Quantum Mechanics by Steven Weinberg
- Quantum Theory for Mathematicians by Brian C. Hall
- Principles of Quantum Mechanics by R. Shankar
- Modern Quantum Mechanics by J.J. Sakurai
- Topics in Quantum Mechanics by David Tong
Quantum Field Theory
- What is a Quantum Field Theory?-A First Introduction for Mathematicians by Michel Talagrand
- Quantum Field Theory-A Tourist Guide for Mathematicians by Gerald B. Folland
- Quantum Field Theory and the Critical Phenomena by Jean Zinn-Justin
- An Introduction to Quantum Field Theory by Michael E. Peskin and Daniel V. Schroeder
- Quantum Field Theory by Mark Srednicki
- Quantum Field Theory and the Standard Model by Matthew D. Schwartz
- The Quantum Theory of Fields by Steven Weinberg
- Quantum Field Theory-A Modern Perspective by V. Parameswaran Nair
- Quantum Field Theory in a Nutshell by A. Zee
- The Global Approach to Quantum Field Theory by Bryce DeWitt
- Stochastic Quantization by Pout H. Damgaard and Helmuth Huffel
- Quantum Field Theory by David Tong
- Quantum Field Theory by Sidney Coleman
- Quantum Field Theory I by Arthur Hebecker
- Quantum Field Theory by Liam Fitzpatrick
- Quantum Field Theory by Timo Weigand
- 6 Lectures on QFT, RG and SUSY by Timothy J. Hollowood
- Quantum Field Theory II by David Skinner
- The Standard Model by David Tong
Stochastic Partial Differential Equations
- Stochastic Equations in Infinite Dimensions by Giuseppe Da Prato and Jerzy Zabczyk
- A Course on Rough Paths-With an introduction to regularity structures by Peter K. Friz and Martin Hairer
- Stochastic PDEs, Regularity Structures, and Interacting Particle Systems by Ajay Chandra and Hendrik Weber
- Paracontrolled distributions and singular PDEs Massimiliano Gubinelli, Peter Imkeller and Nicolas Perkowski