Compact, self-contained text by noted theorist presents the most fundamental aspects of modern differential geometry as well as the basic tools required for the study of Morse theory. Advanced treatment; analytical rather than topological aspects of Morse theory emphasized. Contents: 1. Smooth Manifolds. 2. Spaces of Affine Connection. 3. Riemannian Spaces. 4. The Variational Properties of Geodesics. Appendix Focal Points. 5. A Reduction Theorem. Index. Unabridged republication of the 1967 edition.
