Bayesian Data Analysis by Gelman et al. (2013) — The Bayesian workflow bible. (copyrighted)
Pattern Recognition and Machine Learning by Christopher M. Bishop (2006) — Likelihoods, graphical models, and Bayes done properly. (copyrighted)
Probability Theory: The Logic of Science by E. T. Jaynes (2003) — The philosophical bedrock of Bayesian probability as extended logic. PDF
Think Bayes by Allen B. Downey (2021) — Bayesian statistics by writing code. Ideal computational on-ramp. Online
Bayesian Reasoning and Machine Learning by David Barber (2012) — Graphical models, inference algorithms, and ML from a Bayesian lens. PDF
Statistical Rethinking by Richard McElreath (2020) — The modern Bayesian workflow explained with clarity and care. (copyrighted)
Information Theory, Inference, and Learning Algorithms by David J.C. MacKay (2003) — Information theory meets Bayesian inference meets ML. A masterwork. PDF