Applied Mathematical Sciences, 80. New York, NY etc.: Springer-Verlag. xiv, 334 p. DM 124.00 (1989).

With this book the author has set himself the task of providing “An introductory book which can be recommended for self-study by the undergraduate student or ordinary working mathematician...”. His underlying educational philosophy is very clearly set forth in the preface, which also reveals an obvious delight in the subject matter.
The text develops the theory from theta functions, and discusses Jacobi’s elliptic functions, elliptic inetrals, Weierstrass elliptic functions and modular transformations. In accordance with the author’s general plan, complex function theory is given a supporting role, and appears late in the book. A large number of carefully worked out examples of applications are included, sometimes in separate chapters, which should make the book especially attractive to anyone teaching prospective mathematical practitioners. Appropriately, the book ends with a section of tables, including BASIC programs to produce them.

Reviewer: H.Martens