This IMA Volume in Mathematics and its Applications SHOCK INDUCED TRANSITIONS AND PHASE STRUCTURES IN GENERAL MEDIA is based on the proceedings of a workshop that was an integral part of the 1990-91 IMA program on Phase Transitions and Free Boundaries. The workshop focused on the thermodynamics and mechanics of dynamic phase transitions that are mainly inertially driven and brought together physicists, metallurgists, mathematicians, engineers, and molecular dynamicists with interests in these problems. Financial support of the National Science Foundation made the meeting pos sible. We are grateful to J .E. Dunn, Roger Fosdick, and Marshall Slemrod for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, .Jr. PREFACE When a body is subjected to a strong shock the material may suffer severe local structural changes. Rapid solidification, liquification, or vaporization can oc cur, and, moreover, complex structural heterogeneity is often left in the wake of the passing wave. Thus, inertially driven shock waves raise fundamental questions involving experiment, theory, and mathematics which bear on phase stability and metastability, as well as on reaction kinetics and appropriate measures of phase structure.