A mathematics textbook providing an introduction to fundamental concepts from the theory of complex variables together with numerous worked examples and applications. The textbook contains both elementary and advanced material which is suitable for a one or two semester course in complex variable theory for beginning graduate students in mathematics, physics, engineering and the sciences. There is sufficient elementary material so that the textbook would be suitable for an upper level undergraduate course in complex variable theory. The textbook contains numerous worked examples and a large number of exercises at the end of each chapter. The appendix C contains hints and answers to over 85 percent of the exercise problems. Some of the more difficult problems are worked out in step-by-step detail. An examination of the table of contents and exercise problems at the end of each chapter will illustrate the variety of applications presented. In addition to fundamentals the reader is provided with an introduction to many specialized topics involving complex variables. The text material concludes with a chapter on the Fourier, Laplace and Z-transforms followed by a chapter on special functions. For additional information and sample pages go to the web site: http://www.math.odu.edu/~jhh/counter8.html.