The 1998-1999 program year of the Japan-U.S. Mathematics Institute at the Johns Hopkins University (Baltimore, MD) was devoted to minimal surfaces, geometric analysis, and symplectic geometry. The program culminated in a week-long workshop and conference to discuss recent developments. This volume is a collection of articles written by the speakers. It presents extended or modified versions of the lectures delivered at the meeting. Each article provides a vivid account of current research.The information given ranges from introductory-level to the most recent results. Of special interest is a long survey article by K. Fukaya on applications of Floer homology to mirror symmetry. Also discussed are new developments on the geometry of constant mean curvature one surfaces in hyperbolic 3-spaces of finite total curvature. The range of topics covered in the volume provides direction for further research in these rapidly developing areas. The book is suitable for graduate students and researchers interested in differential and symplectic geometry.