Bayesian Data Analysis, Third Edition [pdf]
Another good one to read is Statistical Rethinking via <a href="https://xcelab.net/rm/statistical-rethinking/" rel="nofollow">https://xcelab.net/rm/statistical-rethinking/</a>.   A bit easier to understand than Gelman's book, but together, these give you an amazing foundation in modern bayesian analysis.<p>Cam's book, mentioned also in the comments, is also wonderful.