This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows:

- Basic Homotopy;
- H-spaces and co-H-spaces;
- Fibrations and Cofibrations;
- Exact sequences of homotopy sets, actions, and coactions;
- Homotopy pushouts and pullbacks;
- Classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead;
- Homotopy Sets;
- Homotopy and homology decompositions of spaces and maps; and
- Obstruction theory.

The underlying theme of the entire...