This book provides a concise treatment of topics in complex analysis, suitable for a one-semester course. It is an outgrowth of lectures given by the author over the last ten years at the University of Goteborg and Chalmers University of Technology. While treating classical complex function theory, the author emphasizes connections to real and harmonic analysis, and presents general tools that might be useful in other areas of analysis.

The book introduces all of the basic ideas in beginning complex analysis and still has time to reach many topics near the frontier of the subject. The reader is expected to have an understanding of basic integration theory and functional analysis. Many exercises illustrate and sharpen the theory, and extended exercises give the reader an active part in complementing the material presented in the text.