Information Theory
Robert M. Gray, "Entropy and Information Theory"
Thomas M. Cover, Joy. A. Thomas, "Elements of Information Theory"
Yury Polyanskiy, Yihong Wu, ''Lecture Notes on Information Theory''
Stefan M. Moser, ''Advanced Topics in Information Theory (Lecture Notes)''
Probability & Statistics
Patrick Billingsley, ''Probability and Measure''
Noga Alon, Joel H. Spencer, ''The Probabilistic Method''
Roman Vershynin, ''High-Dimensional Probability: An Introduction with Applications in Data Science''
Martin Wainwright, ''High-Dimensional Statistics: A Non-asymptptic Viewpoint''
Yihong Wu, ''Information-Theoretic Methods for High-Dimensional Statistics''
Alexandre B. Tsybakov, "Introduction to Nonparametric Estimation"
Stéphane Boucheron, Gábor Lugosi, "Concentration Inequalities"
Machine Learning
Christopher M. Bishop, ''Pattern Recognition and Machine Learning''
Kevin P. Murphy, ''Machine Learning: A Probabilistic Perspective''
Analysis
Peter D. Lax, "Functional Analysis"
Walter Rudin, "Functional Analysis"
Machine Learning & Statistics