Maximal Supersymmetry and Non-Abelian Gauge Groups

Abstract : I review recent progress in the construction and classification of maximally supersymmetric theories with non-abelian gauge groups. The algebraic framework is based on the underlying exceptional symmetry groups. This has applications for supergravity theories describing flux compactifications as well as for the recently constructed three-dimensional superconformal theories describing the dynamics of multiple M2-branes.