Polycrystalline metals, porous rocks, colloidal suspensions, epitaxial thin films, rubber, fibre reinforced composites, gels, foams, granular aggregates, sea ice, shape-memory metals, magnetic materials, electro- rheological fluids, and catalytic materials are all examples of materials where an understanding of the mathematics on the different length scales is a key to interpreting their physical behavior. In their analysis of these media, scientists coming from a multitude of professions have encountered similar mathematical problems, yet it is rare for researchers in the various fields to meet. The chapters in this volume have emerged from the 1995-1996 program at the Institute for Mathematics and its Applications devoted to Mathematical Methods