Cohomological local-to-global principles and integration in finite- and infinite-dimensional Lie theory

The subject of this thesis is twofold: The first part is the study of local-to-global principles for the continuous Lie algebra (co-)homology of certain infinite-dimensional Lie algebras of geometric origin, specifically, Gelfand-Fuks cohomology and continuous cohomology of gauge algebras. It includes both an exposition to classical results of...