This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on 'Composition Operators on Spaces of Analytic Functions' held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. This book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts. In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established.Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.
