  We propose a way to classify all supersymmetric configurations of D=11
supergravity using the G-structures defined by the Killing spinors. We show
that the most general bosonic geometries admitting a Killing spinor have at
least a local SU(5) or an (Spin(7)\ltimes R^8)x R structure, depending on
whether the Killing vector constructed from the Killing spinor is timelike or
null, respectively. In the former case we determine what kind of local SU(5)
structure is present and show that almost all of the form of the geometry is
determined by the structure. We also deduce what further conditions must be
imposed in order that the equations of motion are satisfied. We illustrate the
formalism with some known solutions and also present some new solutions
including a rotating generalisation of the resolved membrane solutions and
generalisations of the recently constructed D=11 Godel solution.
