Mathematical Logics
Book of Proof by Richard Hammack (a very must-read for mathematical thinking strengthen)
Foundation
Introductory Mathematical Analysis For Business, Economics, and The Life and Social Sciences by Ernest F. Haeussler (recommended for non-maths background students to start)
Mathematics for Economists by Simon & Blume
Principal of Mathematical Analysis by Walter Rudin
Mathematics for Economics and Business by Ian Jacques
Essential Mathematics for Economic Analysis by Sydsæter, Hammond, Strøm, and Carvaja
Further mathematics for economic analysis by Sydsaeter, K., Seierstad, A. & Strom, A.
Lecture Notes: Mathematics for Economics by Cuong Le-Van and Ngoc Sang Pham
Lecture Notes for Crash Math Course, a crash Maths course by Prof. Nicolas Vieille in Master in Economics at IP Paris (École Polytechnique & ENSAE)
Real Analysis
Introduction to Analysis (an internal textbook for Bachelor in Mathematics at l'École Polytechnique)
An Introduction to Analysis by Robert C. Guning
Real and Complex Analysis by Walter Rudin
Analyse réelle et complexe by Francois Golse,Yves Laszlo,Claude Viterbo (in French)
Static and Dynamic Optimization
A First Course in Optimization Theory by Sundaram
Finite Dimensional Convexity and Optimization (Monique Florenzano, Cuong Le Van)
An Introduction to Mathematical Optimal Control Theory, Spring, 2024 version by Lawrence C. Evans (University of California, Berkeley)
Recursive Methods in Economic Dynamics (a great textbook for economic analysis)
Optimal Control Theory with Applications in Economics by Thomas A. Weber
Dynamic optimization: the calculus of variations and optimal control in economics and management by Morton I. Kamien
Probability
Probability: Theory and Examples by Rick Durrett
Statistics Inference by Walter Rudin
Probability and Measure by Billingsley
Probability with Martingales by David Williams
Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J. Bierens
(These above books are in the recommended reading list for the crash course in Probability Theory in my Master in Economics at IPP (EP & ENSAE), taught by Prof. Michele Fabi. You can find full course materials here)
Probability and Statistics for Economists by Bruce Hansen