This book examines one of the most exciting but most difficult questions in modern dynamical systems theory - chaotic billiards. In physics, using billiard models, various mechanical processes, molecular dynamics and optical phenomena are described. Over the past thirty-five years, significant advances have been made in the theory of chaotic billiard, but due to the scattering of the main results in inaccessible scientific articles, it remains difficult for beginners. This is the first and so far the only book that fully and systematically sets out all the basic facts about chaotic billiards. The book contains all the necessary definitions, complete proofs of all major theorems, and many examples and illustrations to help the reader understand the material. Hundreds of carefully designed exercises allow the reader not only to get acquainted with chaotic billiards, but also to learn this topic.