This book provides an overview of the physical phenomena discovered in magnetic molecular materials over the last 20 years. It is written by leading scientists having made the most important contributions to this active area of research. The main topics of this book are the principles of quantum tunneling and quantum coherence of single-molecule magnets (SMMs), phenomena which go beyond the physics of individual molecules, such as the collective behavior of arrays of SMMs, the physics of one-dimensional single–chain magnets and magnetism of SMMs grafted on substrates. The potential applications of these physical phenomena to classical and quantum information, communication technologies, and the emerging fields of molecular spintronics and magnetic refrigeration are stressed. The book is written for graduate students, researchers and non-experts in this field of research.