A systematic treatment of the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory - avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasised. The text contains material from the authors earlier book, Algebraic Topology: An Introduction (GTM 56), together with almost all of the now out-of- print Singular Homology Theory (GTM 70) - all of it naturally carefully revised, and brought up to date.
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