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.
