The problem of the electronic structure of solid matter is addressed in terms of multiple scattering theory, starting from a short review of local density functional theories, the properties of Schrodinger and Dirac Hamiltonians for a central field, and resolvents and Green functions. Throughout this book, both ordered and disordered systems are considered, as well as non-relativistic and relativistic schemes. Also discussed are the direct applications of multiple scattering to important aspects of modern materials science, such as band structure spectroscopy (XES, XPS, ARUPS, AES), to Fermi energy related properties (specific heat, electron-phonon enhancement, nuclear spin lattice relaxation, conductivity), and the present understanding of magnetic systems.