Well-written textbooks (or even theses) are the fastest way to learn technical topics that have achieved critical mass. Inspired by a similarly titled post on LessWrong, I have my own evolving list.
For obvious reasons, I have not read most books cover to cover. I have, however, read a few chapters of each to be convinced that the rest of the book would be worth reading. Often, multiple books cater to overlapping topics, and provide complementary strengths to aid understanding. When multiple books are specified within each (sub-)section, it is safe to assume that as a "soft" recommendation order.
Linear Algebra Done Right by Sheldon Axler (1995; 2015)
Introduction to Linear Algebra by Gilbert Strang (1993; 2016)
Convex Optimization by Stephen Boyd and Lieven Vandenberghe (2004)
Numerical Optimization by Jorge Nocedal, Stephen J. Wright (2000; 2006)
Introduction to Partial Differential Equations by Peter J. Olver (2014; 2016)
Partial Differential Equations: An Introduction by Walter A. Strauss
Information Theory, Inference and Learning Algorithms by David J. C. MacKay (2003)
Machine Learning: a Probabilistic Perspective by Kevin Patrick Murphy (2012)
Bayesian Reasoning and Machine Learning by David Barber (2012)
Bayesian Data Analysis by Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin (1995; 2013)