This volume was edited by Russell I. Hemley in preparation for a short course by the same title, organized together with 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. This is number 37 in the Reviews in Mineralogy series, begun in 1974 and continuing with vigor, at least into the near future, with volumes on "Uranium Mineralogy and Geochemistry," on "Sulfate Mineralogy," and on "Natural Zeolites" planned for 1999 and 2000. Volume 36 (1056 pagesl), "Planetary Materials," edited by 1.1. Papike, appeared earlier this year, and it is certainly not unrelated to the subject of this volume on the physics and chemistry of the deep interior of one of the planets. Rus Hemley has highlighted Reviews in Mineralogy Volumes 14, 18, 20 and 29 as particularly relevant to the subject matter of "Ultrahigh-Pressure Mineralogy."