This book provides a comprehensive overview of the fascinating recent developments in atomic- and nanoscale magnetism, including the physics of individual magnetic adatoms and single spins, the synthesis of molecular magnets for spintronic applications, and the magnetic properties of small clusters as well as non-collinear spin textures, such as spin spirals and magnetic skyrmions in ultrathin films and nanostructures. Starting from the level of atomic-scale magnetic interactions, the book addresses the emergence of many-body states in quantum magnetism and complex spin states resulting from the competition of such interactions, both experimentally and theoretically. It also introduces novel microscopic and spectroscopic techniques to reveal the exciting physics of magnetic adatom arrays and nanostructures at ultimate spatial and temporal resolution and demonstrates their applications using various insightful examples. The book is intended for researchers and graduate studentsinterested in recent developments of one of the most fascinating fields of condensed matter physics.