This is a monograph on Bayesian optimization. The book aims to provide a self-contained and comprehensive introduction to Bayesian optimization, starting “from scratch” and carefully developing all the key ideas along the way. The intended audience is graduate students and researchers in machine learning, statistics, and related fields. However, I also hope that practitioners and researchers from more distant fields will find some utility here. The book is divided into three main parts, covering: theoretical and practical aspects of Gaussian process modeling, the Bayesian approach to sequential decision making, and the realization of practical and effective optimization policies. A few additional topics are also covered: an overview of theoretical convergence results, a survey of notable extensions, a comprehensive history of Bayesian optimization, and an annotated bibliography of applications.