Generalised Geometry, Type II Supergravities and Consistent Truncations

The thesis deals first with the basic geometric structures of the generalised tangent bundle E~TM⊕T*M, such as the natural metric, the generalised metric and the Dorfman derivative. It deals then with the reformulation of the NS-NS sector of Type IIA and Type IIB supergravity theories as a generalised geometrical analogue of general relativity by means of a generalised Levi-Civita connection. Finally it focuses on the generalised Scherk- Schwarz reductions in the context of the problem of the consistent truncations, about which we also derive some basic original results. In this context we also explore the use of Inonu-Wigner contractions to construct new examples of consistent truncations starting from some of the ones that are already known, i.e. from reductions on compact Lie groups.