In this thesis a new formulation is presented of the low energy, supergravity limit of type
II string theory and M theory, including fermions to leading order. This is performed by
utilising the language of generalised geometry, which is shown to be the natural setting for
these theories.
The core idea behind generalised geometry – an extension of ordinary differential geometry
– and what makes it such a powerful tool for analysing supergravity, is that it recasts
all the bosonic fields of the manifold as the natural geometric symmetries of an enlarged
tangent space. There are two versions of generalised geometry which are of particular interest,
namely O(d, d) generalised geometry which will be used to formulate the NSNS
sector of type II theories, and Ed(d) generalised geometry (also known as exceptional generalised
geometry) which enables the description of eleven-dimensional supergravity. For
both cases, this work will show how one can introduce generalised connections to study the
differential structure of the extended tangent spaces and define novel notions of generalised
curvature. Specifying extra local structure defines a generalised notion of the Riemannian
metric tensor, which contains all the relevant bosonic fields in a single, unified object.
With these tools one can then reformulate the supergravity equations very naturally,
as they become simply the generalised geometry analogue of Einstein gravity. One thus
obtains a formalism which is automatically fully covariant under all the bosonic symmetries
of supergravity. Furthermore, generalised connections are shown to be intimately related to
supersymmetry, with important consequences for future applications. As an example, in the
concluding chapter it will be shown how the classic problem of solving the Killing spinor
equations of supersymmetric compactifications can be equivalently recast as the statement
that the background possesses the generalised analogue of special holonomy.