This book describes general techniques for solving linear partial differential equations by dividing space into regions to which the equations are independently applied and then assembling a global solution from the partial ones. It is intended for researchers and graduate students involved in calculations of the electronic structure of materials, but will also be of interest to workers in quantum chemistry, electron microscopy, acoustics, optics, and other fields. Multiple scattering theory is, in essence, an extension of Huygens's principle to quantum mechanics. In classical physics, it was introduced by Rayleigh to study propagation of heat and electricity in inhomogeneous media. In quantum theory it has been used to study a number of different phenomena, including LEED spectra, defects in crystalline and disordered media, transport phenomena, photoemission spectroscopy, and electronic-structure calculations. The book begins with an intuitive approach to scattering theory and then turns to partial waves and a formal development of multiple scattering theory, with applications to the solid state (muffin-tin potentials and space-filling cells). The authors then present a variational derivation of the formalism and an augmented version of the theory. It concludes with a discussion of the relativistic formalism and a discussion of the Poisson equation. Appendices discuss Green's functions, spherical functions, Moller operators and the Lippmann-Schwinger equation, irregular solutions, and singularities in Green's functions.