The basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to homeomorphism, although most usually classify up to homotopy (homeomorphism being a special case of homotopy).

Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.

1969, Emil Artin, Hel Braun, Introduction to Algebraic Topology, C. E. Merrill Publishing Company,
Professor Emil Artin lectured on algebraic topology during the winter semester of 1959–60.

The material in Chapters 7 (Obstruction Theory and Eilenberg-MacLane Spaces) and 8 (Bordism, Spectra, and Generalized Homology) introduces the student to the modern perspective in algebraic topology.

2002, Allen Hatcher, Algebraic Topology, Cambridge University Press:

Algebraic topology

Meaning

Noun