This volume contains articles based on recent research and experiments concerning Microstructure and Phase Transition collected by the Institute for Mathematics and its Applications. The book provides a selection of current progress in some of the powerful new methods introduced to study questions on the behavior of crystalline solids, as well as recent experimental results. These articles utilize nonlinear theory as a way to understand and control this behavior. Many potentially relevant technological applications are addressed, including shape memory materials, nonlinear dielectrics and ferroelectrics, magnetostrictive materials, composites, or other materials fabricated or devised to promote special properties. This book should be of interest to both applied mathematicians and engineers.