Various infinite-dimensional Lie algebras and Lie groups, including groups of diffeomorphisms and algebras of vector fields, the affine Kac-Moody algebras and groups, Borcherds Lie algebras, algebras of pseudodifferential operators and various generalizations of these, have beautiful connections with other areas of mathematics and physics such as quantum field theory, fluid mechanics, singularity theory, modular forms, the Monster group, and soliton theory, to name just a few. All these topics, as well as other related aspects and applications of Lie theory, are the subject of this program.