"In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine this class of operators. The progress in the theory of subnormal operators that has come about during the last several years grew out of applying the results of rational approximation." from the Preface This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented toward rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook, including exercises. The book requires background in function theory and functional analysis, but is otherwise fairly selfcontained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hyponormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weakstar rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist. Reviews "As we have come to expect of the author, the standard of exposition is extremely high."  Bulletin of the London Mathematical Society "The authors pedagogical, almost conversational style makes this book a pleasure to read; even experts in subnormal operator theory will want this book as a reference ... the author has developed in this text the theory of subnormal operators with clarity and humor. Anyone interested in operator theory or related areas of functional analysis will find this book a valuable reference."  Mathematical Reviews Table of Contents  Preliminaries
 Subnormal operators: The elementary theory
 Function theory on the unit circle
 Hyponormal operators
 Uniform rational approximation
 Weakstar rational approximation
 Some structure theory for subnormal operators
 Bounded point evaluations
