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In the last decade a tremendous progress has taken place in understanding the basis of magnetism, especially in reduced dimensions. In the first part, the fundamentals of magnetism are conveyed for atoms and bulk-like solid-state systems providing a basis for the understanding of new phenomena which exclusively occur in low-dimensional systems as the giant magneto resistance. This wide field is discussed in the second part and illustrated by copious examples. This textbook is particularly suitable for graduate students in physical and materials sciences. It includes numerous examples, exercises, and references.