This new text approaches the problem of the electronic structure of solid matter in terms of multiple scattering theory. It includes a short review of local density functional theories, taking the reader step-by-step through the properties of Schrodinger and Dirac Hamiltonians for a central field, and resolvents and Green functions. Ordered and disordered systems are considered, along with non-relativistic and relativistic schemes. Also discussed are the direct applications of multiple scattering to important aspects of materials science such as band structure spectography, Fermi energy related properties, and the present understanding of magnetic systems. An ideal resource for solid state physicists and materials scientists, this work may also serve as a text for graduate-level students.