  We survey the history of totally positive matrices and the generalization to
Lie groups. We describe a reduction of a bilinear form to a canonical form
(generalizing the case of symplectic nondegenerate forms) using ideas from
total positivity; we also place this in a Lie group context. We give a short
exposition of results of Fock and Goncharov on the study of homomorphisms of
the fundamental group of a closed surface into a Lie group.
