© 1991

A Basic Course in Algebraic Topology

  • 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 Graduate Texts in Mathematics book series (GTM, volume 127)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. William S. Massey
    Pages 1-34
  3. William S. Massey
    Pages 35-59
  4. William S. Massey
    Pages 60-85
  5. William S. Massey
    Pages 117-146
  6. William S. Massey
    Pages 147-157
  7. William S. Massey
    Pages 158-185
  8. William S. Massey
    Pages 225-253
  9. William S. Massey
    Pages 254-278
  10. William S. Massey
    Pages 279-304
  11. William S. Massey
    Pages 305-322
  12. William S. Massey
    Pages 323-349
  13. William S. Massey
    Pages 350-393
  14. Back Matter
    Pages 407-431

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. 


dimension finite homology volume algebra algebric topology cohomology cohomology theory group

Authors and affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA

About the authors

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
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-97430-9
  • eBook ISBN 978-1-4939-9063-4
  • Series ISSN 0072-5285
  • Series E-ISSN 2197-5612
  • Edition Number 1
  • Number of Pages XVIII, 431
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site