This book provides a comprehensive and self-contained introduction to reversible and quantum circuits, with which power emissions can be reduced or eliminated and processing can be performed exponentially faster compared to conventional methods. No previous knowledge of quantum mechanics is assumed, so the presentation will be accessible to students in electrical engineering, computer science, and mathematics as well as professionals new to this field. After a step-by-step introduction, the necessary background on both reversible and quantum computation is presented, core applications and physical realizations are discussed and automatic design methods for the respective circuits are described. Exercises at the end of each chapter allow the reader to gain deeper insight into the material presented and references are provided to RevKit, an open source toolkit for the design of reversible circuits. This allows the reader to apply the concepts introduced in the book and get hands-on experience by designing their own circuits and algorithms. Presentation slides, covering the content of the book are also available, facilitating the use of the material in courses.