This volume is a collection of research-and-survey articles by specialists in various areas of current research in the theory of analytic functions. Many of these articles emerged essentially from the proceedings of, and various deliberations at, three recent conferences in Japan and Korea: an International Seminar on Current Topics in Univalent Functions and Their Applications which was held in August 1990, in conjunction with the International Congress of Mathematicians at Kyoto, at Kinki University in Osaka; an International Seminar on Univalent Functions, Fractional Calculus, and their Applications which was held in October 1990 at Fukuoka University; and also the Japan-Korea Symposium on Univalent Functions which was held in January 1991 at Geongsan National University in Chinju.