Books.md

Calculus/Real Analysis:

Spivak - Calculus.

Complex Analysis:

Cartan - Théorie Élémentaire des Functions Analytiques dune ou Plusieurs Variables Complexes.

Remmert - Theory of Complex Functions.

Combinatorics/Graph Theory:

Murty - A First Course in Graph Theory and Combinatorics.

Stochastic Processes:

Papoulis - Random Variables and Stochastic Processes.

Kijima - Stochastic Processes with Applications to Finance.

Risk Theory:

Klugman - Loss Models From Data to Decisions.

Measure Theory/Lebesgue Integration:

Taylor - An Introduction to Measure Theory and Integration.

Halmos - Measure Theory.

Probability Theory:

Billingsley - Probability and Measure.

Klenke - Probability Theory a Comprehensive Course.

Feller - An Introduction to Probability Theory and Its Applications.

Extreme Value Theory (Subtopic of Probability Theory):

Leadbetter - Extremes and Random Properties of Random Sequences and Processes.

Game Theory:

Tirole - Game theory (1,2 and 3).

Dynamical System and Chaos:

Devaney - An Introduction to Chaotic Dynamical Systems

Qualitative Theory of the Differential Equations:

Braun - Differential Equations and Their Applications.

Hirsch - Differential equations, Dynamical Systems, and Linear Algebra.

Statistical Methods in Data Mining:

Hastie - The Elemens of Statistical Learning Data Mining, Inference, and Prediction.

Functional Analysis:

Rudin - Functional Analysis.

Statistical Inference:

Casella - Statistical Inference.

Mathematical Finance (Volatility Smiles):

Hafner - Stochastic Implied Volatility.

Bayesian Econometrics:

Bayesian Statistics : An Introduction - Peter Lee

Introduction to Bayesian Econometrics - Edward Greenberg

Options (Very Low Maths):

Passarelli - Trading Option Greeks.

Financial Derivatives:

Hull - Options, Futures and Other Derivatives

Steven Blyth - Introduction to Quantitative Finance

Ross's Recommendations:

Financial Calculus - Baxter

Applied Econometrics - Asteriou and Hall

https://www.risk.net/

My recommendations:

Stochastic Calculus of Variations in Mathematical Finance - Malliavin and Thalmaier

Stochastic Calculus for Finance Parts I and II - Shreve

C++ for Financial Maths https://nms.kcl.ac.uk/john.armstrong/courses/courses.html