In the past century, different branches of mathematics have become more widely separated. Yet, there is an essential unity to mathematics which still springs up in fascinating ways to solve interdisciplinary problems. This text provides a bridge between the subjects of algebraic topology, including differential topology, and geometry. It is a survey book dedicated to a large audience of researchers and graduate students in these areas. Containing a general introduction to the algebraic theory of rational homotopy and giving concrete applications of algebraic models to the study of geometrical problems, mathematicians in many areas will find subjects that are of interest to them in the book.

1. Lie Groups and Homogeneous Spaces; 2. Minimal Models; 3. Manifolds; 4. Complex and Symplectic Manifolds; 5. Geodesics; 6. Curvature; 7. G-Spaces; 8. Blow-ups and Intersection Products; 9. A Florilège of Geometric Applications; Appendices; A. De Rham Forms; B. Spectral Sequences; C. Basic Homotopy Recollections

Yves FélixProfesseur, Université Catholique de Louvain, John OpreaProfessor of Mathematics, Cleveland State University, Daniel TanréProfesseur, Université des Sciences et Technologies de Lille