Volume 37 of Reviews in Mineralogy, divided into three sections, begins with an overview (Chapter 1) of the remarkable advances in the ability to subject minerals-not only as pristine single-crystal samples but also complex, natural mineral assemblages-to extreme pressure-temperature conditions in the laboratory. These advances parallel the development of an arsenal of analytical methods for measuring mineral behavior under those conditions. This sets the stage for section two (Chapters 2-8) which focuses on high-pressure minerals in their geological setting as a function of depth. This top-down approach begins with what we know from direct sampling of high-pressure minerals and rocks brought to the surface to detailed geophysical observations of the vast interior. The third section (Chapters 9-19) presents the material fundamentals, starting from properties of a chemical nature, such as crystal chemistry, thermochemistry, element partitioning, and melting, and moving toward the domain of mineral physics such as melt properties, equations of state, elasticity, rheology, vibrational dynamics, bonding, electronic structure, and magnetism. The Review thus moves from the complexity of rocks to their mineral components and finally to fundamental properties arising directly from the play of electrons and nuclei.This volume was prepared for a short course by the same title, organized by Russell J. Hemley and Ho-kwang Mao and sponsored by the Mineralogical Society of America, December 4-6, 1998 on the campus of the University of California at Davis.