A quote attributed to Mark Twain says that a classic is a book that everyone praises but no one reads. This book, however, is a counterexample to the claim, for it is truly a classic, and one that has played an important role in the education of many mathematicians.

As a standard text on the basic concepts in complex variables, a topic well known to many people, it is probably not essential to give a detailed description of its contents, but a brief one is in order. The first chapter begins with a basic introduction to complex numbers at a level that most people who have studied mathematics in college are likely to be familiar with, covering sequences and series, power series, and the like. The second chapter covers analytic functions, including integration and differentiation in the complex plane, Cauchy’s integral formula, the maximum modulus theorem, and Taylor series. The third chapter, a brief one, deals with contour integration, preparing the ground for the longer fourth chapter on conformal mappings. Chapters 5 through 7 cover special functions such as the gamma function, Laplace’s method and other asymptotic methods, and transform methods such as the Fourier transform, with the final chapter presenting some special topics such as the Wiener-Hopf technique (extremely useful in many engineering and mathematical physics applications).

The text is suitable for use in a class of beginning graduate students or advanced undergraduates, though instructors may wish to focus on or choose only certain chapters, depending on the focus of the course. The first few chapters that present introductory content will likely be useful to most instructors, but a class taught to students studying electrical engineering will probably focus on different parts of chapters 5 through 7 than a class on mathematical physics. Covering the whole book in one semester is par for the course in a graduate class, but might require too brisk a pace for undergraduates. Instructors who have used this book as a teaching resource claim that the exercises given in it are insufficient to sustain the teaching and the assignments to be given, so other companion resources are needed. Other resources are also necessary for more up-to-date information on recent research and applications in the areas covered.