Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. ""Calculus of Variations in the Large"" is certainly one of the essential references on Morse theory.
The fixed end point problem in non-parametric form General end conditions The index form Self-adjoint systems The functional on a Riemannian space The critical sets of functions The boundary problem in the large Closed extremals Solution of the Poincare continuation problem.