Magnetic interactions are not only fascinating from an academic viewpoint, they also play an increasingly important role in chemistry, especially in the chemistry that is aimed at designing materials with prede?ned properties. Many of these materials are magnetic, either in their ground states or by external perturbation and have found their way into real-world applications as molecular switches, sensors or memories. Although magnetic interactions are commonly orders of magnitude weaker than other interactions like covalent bonding, due to these interactions small changes in composition or external conditions may have huge consequences for the properties. Think for example of perovskite-type manganese oxides, where chemical doping affects the interplay between magnetic and electric properties, leading to giant or collossal magnetic resistance. An obvious example dealing with molecular (non-bulk) moieties can be found in the design of single-molecule magnets. Obtaining systems with tailor-made properties heavily depends on our knowledge of the interactions between local magnetic sites. This textbook aims to explain the theoretical basis of magnetic interactions at a level that will be useful for master’s students in chemistry. Although it has been written as a volume in the series “Theoretical and Computational Chemistry”, the book is intended to be also helpful for students of physical, inorganic and organic chemistry. Most chemistry textbooksgiveonly abrief general introduction, whereas textbooks treating magnetic interactions at a more advanced level are mostly written from the perspective of solid-state physics, aiming at physics students.