Preliminary definitions -- Multiple scattering -- Shape functions -- Non-relativistic single-site scattering for spherically symmetric potentials -- Non-relativistic full potential single-site scattering -- Spin-polarized non-relativistic single-site scattering -- Relativistic single-site scattering for spherically symmetric potentials -- Relativistic full potential single-site scattering -- Spin-polarized relativistic single-site scattering for spherically symmetric potentials -- Spin-polarized relativistic full potential single-site scattering -- Scalar-relativistic single-site scattering for spherically symmetric potentials -- Scalar-relativistic full potential single-site scattering -- Phase shifts and resonance energies -- Structure constants -- Green’s functions: an in-between summary -- The Screened KKR method for two-dimensional translationally invariant systems -- Charge and magnetization densities -- The Poisson equation and the generalized Madelung problem for two- and three-dimensional translationally invariant systems -- “Near field” corrections -- Practical aspects of full-potential calculations -- Total energies -- The Coherent Potential Approximation -- The embedded cluster method -- Magnetic configurations — rotations of frame -- Related physical properties.Addressing graduate students and researchers, this book gives a very detailed theoretical and computational description of multiple scattering in solid matter. Particular emphasis is placed on solids with reduced dimensions, on full potential approaches and on relativistic treatments. For the first time approaches such as the Screened Korringa-Kohn-Rostoker method that have emerged during the last 5 – 10 years are reviewed, considering all formal steps such as single-site scattering, structure constants and screening transformations, and also the numerical point of view. Furthermore, a very general approach is presented for solving the Poisson equation, needed within density functional theory in order to achieve self-consistency. Going beyond ordered matter and translationally invariant systems, special chapters are devoted to the Coherent Potential Approximation and to the Embedded Cluster Method, used, for example, for describing nanostructured matter in real space. In a final chapter, physical properties related to the (single-particle) Green’s function, such as magnetic anisotropies, interlayer exchange coupling, electric and magneto-optical transport and spin-waves, serve to illustrate the usefulness of the methods described.