Topology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid-state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. The goal of this book is to provide in concise form the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.