Each locally compact group, commutative or not,
(this includes finite groups and Lie groups) has a dual object which
completely determines it. This object is a commutative
semigroup which is partially ordered and convex. This duality
theory generalizes the Pontryagin-Van Kampen duality for abelian,
locally compact groups in a natural way. We will give a short history,
some examples and indications of proofs.