List will be updated regularly.
Algorithms and complexity
Introduction to Algorithms, third edition - Thomas H. Cormen
Tons of proofs, exercises and graphics. THE book to learn algorithms. A bit maths heavy but nothing wild.
Algorithm Design: Pearson New International Ed - J. Kleinberg
This book takes more time and space to explain topics than Introduction to Algorithms. Contains fewer maths heavy proofs and more practical applications.
Introduction to Graph Theory Taschenbuch - Richard J Trudeau
A short pure maths book for non-mathematicians. I loved every bit of this book and its exercises.
Linear algebra done right - Sheldon Axler
This book is not for people with little time. And definitively not for people without any experience with linear algebra.
Principles of Mathematical Analysis - Walter Rudin
Seriously, this book (also known as Baby Rudin) kicks ass. I don’t even want to know how big Rudin would be.
Probability and statistics
Lectures on probability theory and mathematical statistics - Marco Taboga
A very detailed book on probability theory and statistics with a good mixture of proofs and exercises. A perfect book as reference since every chapter was written independent.
Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan - John Kruschke
Excellent introduction into bayesian statistics without too much mathematics.
An Introduction to Generalized Linear Models - Annette J. Dobson
Probably the best book on GLM. Heavy maths and very many exercises.
Statistik der Weg zur Datenanalyse - Ludwig Fahrmeier
A practical book on statistics with a focus on connecting theoretical concepts and applying them for problem solving.
Einführung in die Wahrscheinlichkeitstheorie und Statistik (vieweg studium; Aufbaukurs Mathematik) (German Edition)
Short and rigorous introduction to probability theory without any measure theory.