The first English edition of this magnificent textbook, translated from Russian, was published in three substantial volumes of 459, 347, and 374 pages, respectively. In this second English edition all three volumes have been put together with a new, combined index and bibliography. Some corrections and revisions have been made in the text, primarily in Volume II. Volumes II and III contain numerous references to the earlier volumes, so that the reader is reminded of the exact statements (and proofs) of the more elementary results made use of. The three-volume-in-one format makes it easy to flip back the pages, refresh one's memory, and proceed. The proofs chosen are those that give the student the best 'feel' for the subject. The watchword is clarity and straightforwardness. The author was a leading Soviet function-theorist: It is seldom that an expert of his stature puts himself so wholly at the service of the student. This book includes over 150 illustrations and 700 exercises.