This book introduces the reader into the field of automata theory and logic. It studies fundamental properties like complementation and determinisation of automata on infinite words and trees, and presents their applications for logics used in program verification. The presentation of such concepts & some of which are 50 years old or more & is given in a modern style and is accompanied by many exercises. The book can be used for self-study or as a basis for a graduate course on automata and logic, presupposing knowledge on finite automata and regular languages of finite words only.