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A Basic Course in Algebraic Topology

  • Textbook
  • © 1991


  • Features topics such as the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory
  • Consists of material from the author's earlier titles, Algebraic Topology (GTM 56) and Singular Homology Theory (GTM 70)
  • Gives several applications of the methods of algebraic topology to concrete geometrical-topological problems

Part of the book series: Graduate Texts in Mathematics (GTM, volume 127)

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About this book

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date. 

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Table of contents (15 chapters)

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    William S. Massey

About the author

William S. Massey (1920-2017) was an American mathematician known for his work in algebraic topology. The Blakers-Massey theorem and the Massey product were both named for him. His textbooks Singular Homology Theory and Algebraic Topology: An Introduction are also in the Graduate Texts in Mathematics series.

Bibliographic Information

  • Book Title: A Basic Course in Algebraic Topology

  • Authors: William S. Massey

  • Series Title: Graduate Texts in Mathematics

  • DOI:

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 1991

  • Hardcover ISBN: 978-0-387-97430-9Published: 06 March 1991

  • eBook ISBN: 978-1-4939-9063-4Published: 28 June 2019

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVIII, 431

  • Topics: Algebraic Geometry

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