Quasielastic neutron scattering has made many important contributions to the atomistic elucidation of diffusion processes in solids. The aim of this book is to inform researchers in solid state physics, solid state chemistry, and inorganic materials science of the potential of quasielastic neutron scattering. The book has been written for experimentalists and contains in its first part the theoretical background on neutrons, neutron scattering, and solid state diffusion, which is essential for the proper use of quasielastic neutron scattering. This general part should be useful for non-experts in the field of neutron scattering and diffusion as well. The second part of the book addresses the experts in this vivid field of research. It summarizes the scientific applications of quasielastic neutron scattering to special solid state materials systems, as for example to hydrogen in metals or to diffusion in solid state ionic conductors.