The study of hyperbolic systems is a core theme of modern dynamics. On surfaces the theory of the fine scale structure of hyperbolic invariant sets and their measures can be described in a very complete and elegant way, and is the subject of this book. The present book, written by well-known experts in smooth dynamical systems and ergodic theory, provides a largely self-contained, rigorous description of this theory. It covers the most important aspects of the subject and is based on several scientific works of the leading research workers in this field. This book fills a gap in the literature of dynamics and is highly recommended for any PhD students interested in this area.