The first German edition of Seifert and Threlfall's "Lehrbuch der Topologie" was published in 1934. The book very quickly became the leading introductory textbook for students of geometric-algebraic topology (as distinguished from point set or "general" topology), a position which it held for possibly 30 to 35 years, during which lime it was translated into Russian. Chinese, and Spanish. An English language edition is. then, long overdue. The translation presented here is due to Michael A. Goldman.
In spite of the fact that with the passage of time our understanding of the subject matter has changed enormously (this is particularly true with regard to homology theory) the book continues to be of interest for its geometric insight and leisurely, careful presentation with its many beautiful examples which convey so well to the student the flavor of the subject. In fact, a quick perusal of the more successful modern textbooks aimed at advanced undergraduates or beginning graduate students reveals, inevitably, large blocks of material which appear to have been inspired by if not directly modeled on sections of this book. For example: the introductory pages on the problems of topology, the classification of surfaces, the discussion of incidence matrices and of methods for bringing them to normal form, the chapter on 3-dimcnsionaI manifolds (in particular the discussion of lens spaces), the section on intersection theory, and especially the notes at the end of the text have withstood the test of time and are as useful and readable today as they no doubt were in 1934.
This volume contains, in addition to Seifert and Threlfall's book, a translation into English, by Wolfgang Heil, of Seifert's foundational research paper "The topology of 3-dimensional fibereel spaces" ("Topologie dreidi-mensionales gefaserler Raum," Ada Mathematica 60. 147 288 (1933)]. The manuscript treats a simple and beautiful question: what kinds of 3-dimensional manifolds can be made up as unions of disjoint circles, put together nicely?