<P>This book provides a thorough introduction to homogenization, a modeling procedure used to describe processes in complicated structures with known microstructures. It first presents the theoretical foundations of this powerful tool of analysis. Building on the theory, the authors explore various types of application problems, including flow in porous media, sound propagation in fluid saturated solids, acoustics of granular material, computational multiscale finite element methods, and interfaces in viscoelastic materials. The book also discusses results in which G-limits have different structures from the initial operators.</P>