Semimagnetic semiconductors (SMSC) and diluted magnetic semiconductors (DMS) have in the past decade attracted considerable attention because they confer many new physical properties on both bulk materials and heterostructures. These new effects are due either to exchange interactions between magnetic moments on magnetic ions, or to exchange interactions between magnetic moments and the spin of the charge carrier. These effects vary with the transition metal (Mn, Fe, Co) or rare earth (Eu, Gd, etc) used and thus provide a range of different situations. The field is very large (zero gap, small gap, wide gap), and the magnetic properties also are very rich (paramagnetic spin glass, antiferromagnetism). These materials are very convenient for studying the magnetism (the magnetism is diluted) or the superlattices (SL) with a continuous change from type II SL to type III SL. This Course attempted to provide a complete overview of the topic. The participants of this summer school held in Erice came from ten countries and were from various backgrounds and included theoreticians, experimentalists, physicists, and chemists. Consequently, an attempt was made to make the Course as thorough as possible, but at the same time attention was devoted to basic principles. The lecturers, drawn from all the groups in the world involved in the field, were asked to be very didactic in their presentation. After two introductory lectures, Dr.