A new approach that treats complex analysis in a broad contextThis book presents a new approach to one of mathematics' oldest fields. It departs from the tradition of teaching complex analysis as a self-contained subject and, instead, treats the subject as a natural development from calculus. It also shows how complex analysis is used in other areas, exploring connections with calculus, algebra, geometry, topology, and other parts of analysis.The authors provide the ideal framework for a first-year graduate course in complex analysis—building upon ideas the student is already familiar with and simplifying the transition to advanced topics. The book is also for those using complex numbers and functions in applied fields, including engineering, physics, and other areas.Function Theory of One Complex VariableCompares and contrasts complex variable theory with real variable theoryClarifies analytical ideas belonging to complex analysis by separating them from topological issuesDiscusses some of the current research in the field, including a number of interesting topics not discussed in other textbooksFeatures many examples as well as 75 illustrationsProvides especially thorough exercise setsROBERT E. GREENE is a professor in the Department of Mathematics at the University of California at Los Angeles.STEVEN G. KRANTZ is a professor in the Department of Mathematics at Washington University in St. Louis, Missouri.