This text presents a detailed view of the calculation methods involved in the magnetic properties of transition metal complexes. Starting at an elementary level, it proceeds gradually through theory and calculations to offer sufficient background for original work in the field. No specialized knowledge of magnetism is assumed in the introductory chapters, which offer basic definitions and generalizations of magnetic behavior and briefly review both crystal field theory and perturbation theory. Succeeding chapters explore calculations of the magnetic properties of cubic and axially distorted complexes. Featuring the complete calculation for spin-orbit coupling and magnetic field perturbations for one d-configuration, the text also discusses derivations and results for other configurations. Other topics include the magnetism of polynuclear species, in which antiferromagnetic ordering occurs over small numbers of centers. Detailed calculations by the dipolar coupling approach are given, and the results are applied to a number of studies from the literature.