A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.

Yves Felix, author of books on raional homotopy and more than eighty papers in algebraic topology, received his Ph.D. in 1979. From 1981 to 1989 he worked as a researcher for the FNRS (Belgium) and in 1989 he took up the position of Professor at the Université Catholique de Louvain, which he has held since.; John Oprea received his Ph.D. in 1982 from Ohio State University and has been at Cleveland State University since 1985. His interests lie in both algebraic topology and differential geometry and he has written papers and books in these areas. Oprea was awarded the Lester R. Ford award from the Mathematical Association of America in 1996. He is currently an associate editor for the Journal of Geometry and Symmetry in Physics.; Daniel Tanré received his Ph. D. from the University of Paris in 1972 and has been a Professor at the University of Lille, France, since 1988. He has been an author of books and articles on Algebraic Topology and applications since 1972.

• 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