  Generalised geometry studies structures on a d-dimensional manifold with a
metric and 2-form gauge field on which there is a natural action of the group
SO(d,d). This is generalised to d-dimensional manifolds with a metric and
3-form gauge field on which there is a natural action of the group $E_{d}$.
This provides a framework for the discussion of M-theory solutions with flux. A
different generalisation is to d-dimensional manifolds with a metric, 2-form
gauge field and a set of p-forms for $p$ either odd or even on which there is a
natural action of the group $E_{d+1}$. This is useful for type IIA or IIB
string solutions with flux. Further generalisations give extended tangent
bundles and extended spin bundles relevant for non-geometric backgrounds.
Special structures that arise for supersymmetric backgrounds are discussed.
