  We construct a manifestly diffeomorphism invariant Wilsonian (Exact)
Renormalization Group for classical gravity, and begin the construction for
quantum gravity. We demonstrate that the effective action can be computed
without gauge fixing the diffeomorphism invariance, and also without
introducing a background space-time. We compute classical contributions both
within a background-independent framework and by perturbing around a fixed
background, and verify that the results are equivalent. We derive the exact
Ward identities for actions and kernels and verify consistency. We formulate
two forms of the flow equation corresponding to the two choices of classical
fixed-point: the Gaussian fixed point, and the scale invariant interacting
fixed point using curvature-squared terms. We suggest how this programme may
completed to a fully quantum construction.
