This book is an application of quantum mechanics and statistical mechanics to the field of magnetism. A large part of the book is devoted to a detailed treatment of the connections between electronic properties and magnetism, and how they differ in the various known magnetic systems. Current trends are exposed and explained for a large class of alloys and compounds. The modern field of artificially layered systems - known as multilayers - and their industrial applications are dealt with in detail. The book also relates the rich thermodynamic properties of magnets to the ab initio results originating from the electronic structure.