This tutorial by Peter I. Frazier provides a comprehensive overview of Bayesian optimization, a method for optimizing expensive, black-box functions. The tutorial covers the fundamental concepts, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. It also discusses more advanced techniques such as multi-fidelity optimization, multi-information source optimization, and handling noisy evaluations. The tutorial concludes with a discussion of Bayesian optimization software and future research directions. A key contribution is a novel analysis of expected improvement for noisy measurements, which justifies its use in noisy environments. The tutorial is structured to be accessible to both beginners and advanced users, making it a valuable resource for researchers and practitioners in the field.This tutorial by Peter I. Frazier provides a comprehensive overview of Bayesian optimization, a method for optimizing expensive, black-box functions. The tutorial covers the fundamental concepts, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. It also discusses more advanced techniques such as multi-fidelity optimization, multi-information source optimization, and handling noisy evaluations. The tutorial concludes with a discussion of Bayesian optimization software and future research directions. A key contribution is a novel analysis of expected improvement for noisy measurements, which justifies its use in noisy environments. The tutorial is structured to be accessible to both beginners and advanced users, making it a valuable resource for researchers and practitioners in the field.