The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Seminar in Differential Geometry , Annals of Math. Studies, no. 102, Princeton U. Press). The main subjects are harmonic functions and mapping, Monge-AmpFre equation, differential systems, and minimal submanifolds. No index. Annotation copyright Book News, Inc. Portland, Or.