Provides graduate students and research mathematicians working in algebraic geometry with a perspective on how four-manifold theory was studied before the discovery of the Weiberg-Witten theory in current use. Explains how the spectacular success of the theory was founded on a decade of constructing correct questions and basic strategies. The five lectures are from the 1994 meeting of an annual summer graduate program in Princeton, New Jersey. No index. Members of the Mathematical Association of America and the National Council of Teachers of Mathematics receive a 20% discount from list price. Annotation c. by Book News, Inc., Portland, Or.