"During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a survey of these results and an introduction to the branch of analysis that contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff, and others, appear here in book form for the first time." The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and external length, and each chapter has many exercises to further inform and teach the reader.