The first of the Carus Monographs, Professor Bliss's Calculus of Variations, has for its successor the present volume on Analytic Functions of a Complex Variable. The reader is assumed to have the same preparation as for the preceding monograph, that is to say, an acquaintance with elementary differential and integral calculus. Without such knowledge one may, however, obtain some idea of the scope and purposes of the theory of functions from the following pages. Those should profit most who are familiar with more than the elements of the calculus.

The theory of functions of a complex variable has been developed by the efforts of thousands of workers through the last hundred years. To give even the briefest account of the present state of that theory in all its branches would be impossible within the limits of this book. What is attempted here is a presentation of fundamental principles with sufficient details of proof and discussion to avoid the style of a mere summary or synopsis. In various places there are indications of directions in which special portions of the subject branch off from the main stem. For almost every topic the reader is given several references; and, be it for better or worse, there are no footnotes.

The system of references perhaps needs some defense, certainly it requires explanation. Numerous citations of authorities are favorite means for an author to show his erudition—or someone's else.