  This thesis considers two different aspects of string theory, the tensionless
limit of the string and supersymmetric sigma models. The tensionless limit is
used to find a IIB supergravity background generated by a tensionless string.
Quantization of the tensionless string in a pp-wave background is performed and
the tensionless limit is found to commute with quantization. Further, the sigma
model with N=(2,2) extended world-sheet supersymmetry is considered and the
requirement on the target space to have a bi-Hermitean geometry is reviewed. It
is shown that the equivalence between bi-Hermitean geometry and generalized
Kahler follows, in this context, from the equivalence between the Lagrangian-
and Hamiltonian formulation of the model. Moreover, the explicit T-duality
transformation in the Hamiltonian formulation of the sigma model is constructed
and shown to be a symplectomorphism. Under certain assumptions, the amount of
extended supersymmetry present in the sigma model is shown to be preserved
under T-duality. Further, by requiring N=(2,2) extended supersymmetry in a
first order formulation of the sigma model an intriguing geometrical structure
arises and in a special case generalized complex geometry is found to be
contained in the new framework.
