The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship between modern axiomatic approach and geometric intuition. The text is kept at a concrete level, 'motivational' in nature, avoiding abstractions. A number of intuitively appealing definitions and theorems concerning surfaces in the topological, polyhedral, and smooth cases are presented from the geometric view, and point set topology is restricted to subsets of Euclidean spaces. The treatment of differential geometry is classical, dealing with surfaces in R3 . The material here is accessible to math majors at the junior/senior level.

Review

"[The author] avoids aimless wandering among the topics by explicitly heading towards milestone theorems... [His] directed path through these topics should make an effective course on the mathematics of surfaces. The exercises and hints are well chosen to clarify the central threads rather than diverting into byways."

- Computing Reviews

"Many examples and illustrations as well as exercises and hints to solutions are providing great support... By well-placed appendices the reader is relieved of the strain to immediately understand some extensive proofs or to learn adjoining mathematical facts... The book is suitable for students of mathematics, physics and of the teaching profession as well as university teachers who might be interested in using certain chapters...to present the topic in a seminar or in not too advanced special lectures about the topic...It is the great clarity of thought in this book, the simplicity and concreteness of the representation with respect to the capacity for teaching of students, and some other aspects that make this work stand out from comparable efforts."

- ZAA

"The exposition is clear, nicely organized, and generally easy to read." ---Zentralblatt Math

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