  We reformulate eleven-dimensional supergravity, including fermions, in terms
of generalised geometry, for spacetimes that are warped products of Minkowski
space with a $d$-dimensional manifold $M$ with $d\leq7$. The reformation has a
$E_{d(d)} \times \mathbb{R}^+$ structure group and is has a local $\tilde{H}_d$
symmetry, where $\tilde{H}_d$ is the double cover of the maximally compact
subgroup of $E_{d(d)}$. The bosonic degrees for freedom unify into a
generalised metric, and, defining the generalised analogue $D$ of the
Levi-Civita connection, one finds that the corresponding equations of motion
are the vanishing of the generalised Ricci tensor. To leading order, we show
that the fermionic equations of motion, action and supersymmetry variations can
all be written in terms of $D$. Although we will not give the detailed
decompositions, this reformulation is equally applicable to type IIA or IIB
supergravity restricted to a $(d-1)$-dimensional manifold. For completeness we
give explicit expressions in terms of $\tilde{H}_4=\mathit{Spin}(5)$ and
$\tilde{H}_7=\mathit{SU}(8)$ representations for $d=4$ and $d=7$.
