This volume collects some of the survey lectures delivered at the Microprogram on Noncommutative Rings held at the Mathematical Sciences Research Institute, July 10-12, 1989. While the program was concerned with recent advances in ring theory, it also focussed on related areas of mathematics where ring theory might be expected to have an impact. Topics covered included quantum groups, the algebraic aspects of quantum field theory, finite dimensional Lie algebras, and the modern theory of Noetherian rings and localization. The text will be a valuable tool for both advanced graduate students and research mathematicians.