In this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments."

One of the most eminent of contemporary mathematicians, Shing-Tung Yau has received numerous honors, including the 1982 Fields Medal, considered the highest honor in mathematics, for his work in differential geometry. He is known also for his work in algebraic and Kähler geometry, general relativity, and string theory. His influence in the development and establishment of these areas of research has been great. These five volumes reproduce a comprehensive selection of his published mathematical papers of the years 1971 to 1991—a period of groundbreaking accomplishments in numerous disciplines including geometric analysis, Kähler geometry, and general relativity. The editors have organized the contents of this collection by subject area—metric geometry and minimal submanifolds; metric geometry and harmonic functions; eigenvalues and general relativity; and Kähler geometry. Also presented are expert commentaries on the subject matter, and personal reminiscences that shed light on the development of the ideas which appear in these papers.