"Twenty Lectures ..." is based on a course that Professor Piterbarg, a founder of the asymptotic theory of Gaussian processes and fields, teaches to higher-level undergraduate and graduate students at the Faculty of Mechanics and Mathematics, Lomonosov Moscow State University. Written in a clear and succinct style, the book provides a wide-ranging introduction to the field. The first half of the book is devoted to the general theory of Gaussian distributions in both finite- and infinite-dimensional vector spaces. Fundamental results, such as Slepian's, Fernique-Sudakov's and Berman's inequalities, among many others, are clearly explained from a modern, unified point of view. The second half of the book focuses on asymptotic methods, in particular on distributions of high extrema of Gaussian processes and fields. Foundational tools such as the Double Sum Method, the Method of Moments, and the Comparison Method, invented and popularized by the author, are prominently featured....