  In this lecture I review recent results on the use of Solvable Lie Algebras
as an efficient description of the scalar field sector of supergravities in
relation with their non perturbative structure encoded in the U-duality group.
I also review recent results on the construction of BPS saturated states as
solution of the first differential equations following from imposing
preservation of a fraction of the original supersymmetries. In particular I
discuss N=2 extremal black holes that are approximated by a Bertotti Robinson
metric near their horizon. The extension of this construction to maximally
extended supergravities in all dimensions from 4 to 11 is work in progress
where the use of the Solvable Lie algebra approach promises to be of decisive
usefulness.
