  The purpose of the present thesis is to give a self-contained review of the
solvable Lie algebra approach to supergravity problems related with S, T and U
dualities. After recalling the general features of dualities in both
Superstring theory and Supergravity, we introduce the solvable Lie algebra
formalism as an alternative description of the scalar manifold in a broad class
of supergravity theories. It is emphasized how this mathematical technique on
one hand allows to achieve a geometrical intrinsic characterization of
Ramond-Ramond, Neveu-Schwarz and Peccei-Quinn scalars, once the supergravity
theory is interpreted as the low energy limit of a suitably compactified
superstring theory, on the other hand provides a convenient framework in which
to deal with several non-perturbative problems. Using solvable Lie algebras for
instance we find a general mechanism for spontaneous N=2 to N=1 local
supersymmetry breaking. Moreover solvable Lie algebras are used to define a
general method for studying systematically BPS saturated Black Hole solutions
in supergravity.
