The techniques of magnetic neutron and photon scattering provide information on the electronic properties of materials that is obtainable in no other way. With both techniques information on an atomic scale is obtained on the spatial and temporal developments of the spin and current densities which are fundamental quantities in a basic understanding of magnetic phenomena. To date most magnetic scattering studies have used neutron beams, and the use of photon beams is, relatively speaking, in its infancy. This book is the first monograph devoted to the theory required for a full interpretation of magnetic scattering experiments. It is designed to meet the needs of postgraduates and researchers new to the techniques. At the same time, the requirements of theoretical chemists and physicists are catered for through chapters that present the basic formalism in detail. Special features of the book include extensive tables of quantities that occur frequently in applications of theory, and a number of worked examples.