These notes originated at a seminar that was held during July and August of 1987 at Salt Lake City. The original aim of the seminar was to get an overview of the following three topics:
1. Recent advances in the classification program of three (and higher) dimensional algebraic varieties.
2. Existence of rational curves and other special subvarieties.
3. Existence and nature of special metrics on varieties.
We also hoped to then go further and study the relationships between these three approaches. Time however proved to be insufficient to complete even the limited program.