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.
Computation Geometry: Algorithms and Applications - Mark de Berg [WIP]
The only book I could found about computation geometry. I find the organization of the book sometimes a bit chaotic, but at the end I could learn everything I wanted. 4/5.
Linear Programming: Foundations and Extensions - Robert J. Vanderbei [WIP]
Very good book for linear programming without that much maths, very easy to read and lots of exercises.
Linear Algebra - Gerd Fisher
Excellent book. Really love the exercises.
Analysis 1 - Otto Forster
Covers everything one needs for univariate differentiation und integration.
Linear Algebra done right - Sheldon Axler [WIP]
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 [WIP]
Seriously, this book (also known as Baby Rudin) kicks ass. I don’t even want to know how big Rudin would be.
Stochastik - Hans-Otto Georgii [WIP]
Very rigorous book about probability theory and statistics. The measure theory gave me some trouble, but nothing that Wikipedia could not help.
Probability and statistics
All of statistics: A concise course in statistical inference - Larry Wasserman [WIP]
Short introduction on every possible topic of statistics. Not that suitable for first time interaction with 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 from a rather philosophical aspect.
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.