  This thesis deals with the two duality symmetries of N=2 D=10 supergravity
theories that are descendant from the full superstring theory: fermionic
T-duality and U-duality. The fermionic T-duality transformation is applied to
the D-brane and pp-wave solutions of type IIB supergravity. New supersymmetric
solutions of complexified supergravity are generated. We show that the pp-wave
yields a purely imaginary background after two dualities, undergoes a geometric
transformation after four dualities, and is self-dual after eight dualities.
Next we apply six bosonic and six fermionic T-dualities to the AdS_4 x CP^3
background of type IIA supergravity, which is relevant to the current research
in the amplitude physics. This helps to elucidate the potential obstacles in
establishing the self-duality, and quite independently from that shows us that
fermionic T-dualities may be degenerate under some circumstances. Finally, we
make a step towards constructing a manifestly U-duality covariant action for
D=10 supergravities by deriving the generalized metric for a D1-brane. This is
a single structure that treats brane wrapping coordinates on the same footing
as spacetime coordinates. It turns out that the generalized metric of a
D-string results from that of the fundamental string if one replaces the
spacetime metric with the open string metric. We also find an antisymmetric
contribution to the generalized metric that can be interpreted as a
noncommutativity parameter.
