Theory of Magnetism is an important subfield of the theory of solids, and has guided a long history of research into the phenomenon of magnetism. This book provides the foundation for further development in this field. Its contents are divided into four parts. In Part I, Magnetic Ions in Crystals, the electron states of magnetic ions in crystals and the exchange interactions between them are explained. Part II, Magnetism of Spin Systems, treats problems of ferromagnetism and antiferromagnetism shown by exchange-coupled localized spin systems. In Part III, Magnetism of Metals, magnetic properties of itinerant electron systems are discussed in relation to 3d electrons in iron-group metals. Part IV, Magnetism of Dilute Alloys, is devoted to an explanation of the Kondo effect and related topics.