"A particularly nice feature of this textbook is that throughout, the authors have sprinkled citations of expository pieces taken from the Monthly as well as from Mathematics Magazine, the Intelligencer, and even the Proceedings of the AMS. This is a great source for both students as well as their teachers. The book also is an excellent source of problems, close to 300 in total." Mathematical Association of America "Parts of the new material in the last chapters appear here for the first time in a textbook, making this second edition even rather topical and particularly up-to-date. Each chapter contains many illustrating concrete examples and a large number of related exercises, most of which invite the ambitious reader to complement the material discussed in the text. Now as before, this unusual textbook in complex analysis has maintained its unique character, and the new material added in the second edition makes it even more special, interesting and valuable for further generations of students and teachers." Zentralblatt MATH Review of the First Edition: "… covers an unusually large amount of material in a relatively few pages, and does so in a way that provides an excellent survey of the results and techniques of function theory … the presentation often provides excellent insights into the subject." Mathematical Reviews This volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.