Rational homotopy theory (The book)

Rational Homotopy Theory
by  Yves Félix - Stephen Halperin - Jean-Claude Thomas
GTM 205 (2000) Springer Verlag.

While rational homotopy theory is remarkably computational and simpler than ordinary homotopy theory, it is exactly this simplicity that makes it possible to address a number of fundamental questions in geometry and homotopy theory.

The three main objectives of the book are:

• to provide a coherent, self-contained, and user-friendly introduction to the tools and techniques of rational homotopy theory
• to provide an account of the main structural theorems with proofs that are often new or much simpler than the original versions in the literature
• to illustrate both the use of the mathematical technology and the consequences of the theorems in a rich variety of examples.

It should be emphasized that this book is about topological spaces and that examples and applications given throughout the book are largely drawn from topology. The reader should have a basic knowledge of the fundamental group and singular homology.