Books
Mathematics
Principles of Mathematical Analysis by Walter Rudin (ideal pure math book, precise, smooth, complete, concise)
Probability Models by Sheldon Ross (application of probability and stochastic process, no measure theory)
Nonlinear Dynamics and Chaos by S. H. Strogatz (excellent book, clearly written, very readable)
Evolutionary Dynamics by Martin Nowak (great book, extremely concise, clear and insightful)
Stochastic Processes in Physics and Chemistry by N.G. Van Kampen (best on this subject)
Basic Stochastic Processes by Zdzislaw Brzezniak and Tomasz Zastawniak (concise and clear illustration using measure theory)
Networks: An Introduction by M. E. J. Newman (very clear "Newman-style" book )
Geometry and the Imagination by David Hilbert (a masterpiece, it covers many topics related to soft matter physics)
Probability Theory: The Logic of Science by Edwin Thompson Jaynes (very insightful illustration of how the plausible reason works using Bayesian probability)
Machine Learning
An Introduction to Statistical Learning (link) by James, G., Witten, D., Hastie, T., Tibshirani, R. (excellent introduction to conventional machine learning concepts using R, from the statistics perspective)
The Elements of Statistical Learning by Jerome H. Friedman, Robert Tibshirani, and Trevor Hastie (more rigorous mathematical treatments)
Python Machine Learning by Sebastian Raschka and Vahid Mirjalili (a practical approach using Python, from the academic research perspective) (code on github)
Hands-On Machine Learning with Scikit-Learn and TensorFlow by Aurélien Géron (from the industrial perspective, using Python. After reading this book, you can actually work on real problems!)
Deep Learning by Ian Goodfellow and Yoshua Bengio and Aaron Courville (from the computer science perspective focusing on algorithms)
Physics
Introduction to Modern Statistical Mechanics by David Chandler (concise, modern topic, sharp perspective)
Fundamentals of Statistical and Thermal Physics by Federick Reif (explain basic concepts well)
Equilibrium Statistical Physics by Michael Plischke and Birger Bergersen (modern topic, detailed in basic concepts)
Solid State Physics by N. W. Ashcroft and N. D. Mermin (comprehensive on hard matter)
Principles of Condensed Matter Physics by P. M. Chaikin and T. C. Lubensky (modern topic, soft matter)
Theory of Simple Liquids by J. P. Hansen and I. R. McDonald (comprehensive on simple liquid)
Basic Concepts for Simple and Complex Liquids by J. L. Barrat and J. P. Hansen (concise, clear illustration)
Lectures on Phase Transitions and the Renormalization Group by Nigel Goldenfeld (insightful physics)
Intermolecular and Surface Forces by Jacob N. Israelachvili (molecular and soft matter perspective on forces)
Geometrical Frustration by Jean-François Sadoc and Rémy Mosseri
Polymer Physics by Michael Rubinstein and Ralph H. Colby (clear, comprehensive)
Lecture Notes in Physics by Springer
Quantum Field Theory and Condensed Matter by Ramamurti Shankar (Ising model, renormalization group theory)
Properties of Polymers by D.W. Van Krevelen and K. Te Nijenhuis (comprehensive handbook of polymer properties: structural, optical, electromagnetic, mechanic, transport etc.)
The Theory of Transformations in Metals and Alloys by J.W. Christian
Simulation
Monte Carlo Methods in Statistical Physics by M. E. J. Newman and G. T. Barkema (excellent book on spin models)
Understanding Molecular Simulation by Daan Frenkel and Berend Smit (excellent book on particle-based models)
Computer Simulations of Liquids (Code) by M. P. Allen and D. J. Tildesley (illustrates basic principles of molecular dynamics well)
Computational Physics by Mark Newman (numerical analysis for physicist, with Python)
Programming and Script
The C Programming Language by B. W. Kernighan and D. M. Ritchie (best written programming book)
Numerical Recipes in C by W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (a good library of numerical computation codes)
The Not So Short Introduction to Latex (pdf) by Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl (very helpful, showing both script and output)