This text is based on lectures given by the authors at Helsinki University and at the University of Zürich, and is a translation of the German edition, Enidühung in die Funktionentheorie, published by Birkhäuser Verlag, Basel, in 1964. The book is limited to elements of the theory of functions. Coverage includes complex numbers, the concept of homotopy and its application, integral theorems, the theory and application of harmonic functions, and the correspondence of boundaries under conformal mapping. In introducing elementary functions, the authors have followed the presentation given by Ernst Lindelöf in his Finnish textbook, Johdatus funktioteoriaan. Chapter exercises are included, for a total of 320 exercises. It is assumed that the reader is acquainted with analytic geometry and calculus. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)