This rapid and concise presentation of the essential ideas and
results of algebraic topology follows the axiomatic foundations
pioneered by Eilenberg and Steenrod. The approach of the book is
pragmatic: while most proofs are given, those that are particularly
long or technical are omitted, and results are stated in a form
that emphasizes practical use over maximal generality. Moreover, to
better reveal the logical structure of the subject, the separate
roles of algebra and topology are illuminated. Assuming a
background in point-set topology, Fundamentals of Algebraic
Topology covers the canon of a first-year graduate course in
algebraic topology: the fundamental group and covering spaces,
homology and cohomology, CW complexes and manifolds, and a short
introduction to homotopy theory. Readers wishing to deepen their
knowledge of algebraic topology beyond the fundamentals are guided
by a short but carefully annotated bibliography.
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