The variational theory of geodesics

Riemannian geometry is a fundamental area of modern mathematics, and the subdiscipline of geodesics (shortest paths) is of particular significance. Compact and self-contained, this text by a noted theorist presents the essentials of modern differential geometry as well as the basic tools for the study of Morse theory. The advanced treatment emphasizes analytical rather than topological aspects of Morse theory. Requires a solid background in calculus.