This graduate-level textbook presents an introduction to Bayesian statistics and decision theory. Its scope covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics such as complete class theorems, the Stein effect, hierarchical and empirical Bayes modeling, Monte Carlo integration, and Gibbs sampling. It is the translation of a successful French text. In the translation to the English edition, the author has taken the opportunity to add and update material, and to include many problems and exercises for students.