Global analysis is analysis on Riemannian manifolds.
Analysis here means the study of ordinary and partial differential operators on bundles over such manifolds and its applications. All these theorems were known in the early sixties of this century. This theorem marked the birth of the mathematical field of global analysis. In deed one reason for searching such a theorem was the attempt to unify all the upper results to one and only one formula. Such a formula has been conjectured much earlier by M. Gelfand in the context of the homotopy invariance of the index of a Fredholm operator.