  We show that generalised geometry gives a unified description of bosonic
eleven-dimensional supergravity restricted to a $d$-dimensional manifold for
all $d\leq7$. The theory is based on an extended tangent space which admits a
natural $E_{d(d)} \times \mathbb{R}^+$ action. The bosonic degrees of freedom
are unified as a "generalised metric", as are the diffeomorphism and gauge
symmetries, while the local $O(d)$ symmetry is promoted to $H_d$, the maximally
compact subgroup of $E_{d(d)}$. We introduce the analogue of the Levi--Civita
connection and the Ricci tensor and show that the bosonic action and equations
of motion are simply given by the generalised Ricci scalar and the vanishing of
the generalised Ricci tensor respectively. The formalism also gives a unified
description of the bosonic NSNS and RR sectors of type II supergravity in $d-1$
dimensions. Locally the formulation also describes M theory variants of double
field theory and we derive the corresponding section condition in general
dimension. We comment on the relation to other approaches to M theory with
$E_{d(d)}$ symmetry, as well as the connections to flux compactifications and
the embedding tensor formalism.
