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)
Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, III (1997)
Fundamentals of Matrix Computations by David S. Watkins (2010)
Matrix Computations by G.H. Golub and C.F. Van Loan (2013)
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 (2008)
Pattern Recognition and Machine Learning by Christopher Bishop (2006)
Patterns, Predictions, and Actions: A Story about Machine Learning by Moritz Hardt and Benjamin Recht (2021)
Deep Learning by Ian Goodfellow and Yoshua Bengio and Aaron Courville (2016)
Reinforcement Learning: An Introduction by Richard S. Sutton and Andrew G. Barto (1998; 2018)
Information Theory, Inference and Learning Algorithms by David J. C. MacKay (2003)
Probabilistic Machine Learning by Kevin Murphy (book series 2012, 2021, 2022)
Bayesian Reasoning and Machine Learning by David Barber (2012)
Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams (2006)
Monte Carlo theory, methods and examples by Art Owen (2013)
Foundations of Machine Learning by Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar (2012; 2018)
Understanding Machine Learning: From Theory to Algorithms by Shai Shalev-Shwartz and Shai Ben-David (2014)
Reinforcement Learning: Theory and Algorithms by Alekh Agarwal, Nan Jiang and Sham M. Kakade (2019)
I have not read these books, but keeping here as good introductory references to complex topics when I need them.
Computational Optimal Transport by Gabriel Peyré and Marco Cuturi (2018)
A First Look at Stochastic Processes by Jeffrey S. Rosenthal (2019)
An Introduction to the Numerical Simulation of Stochastic Differential Equations by Desmond Higham and Peter Kloeden (2021)