|dc.description.abstract||This thesis explores the geometry of string theory backgrounds and the nongeometric
features of string theory that arise due to T-duality. For this reason,
it is divided into two complementary parts. Part I deals with the superalgebras
of symmetries of string theory and M-theory backgrounds, the so-called Killing
superalgebras. It is shown that one can define a Lie superalgebra consisting
of the infinitesimal field-preserving isometries and the supersymmetries of the
background. We also explore the extension of a Killing superalgebra with brane
charges. Part II deals with non-geometric backgrounds. In particular, we adopt
the framework of the doubled geometry, also known as the doubled torus. We
analyze the hamiltonian dynamics of the system and quantize a model T-fold.
Finally we extended the doubled torus system to include worldsheet supersymmetry.
Throughout part II, we focus on the equivalence, classical and quantum,
of the doubled formalism with the conventional formulation.||en