  We present a general framework for analyzing spatially inhomogeneous
cosmological dynamics. It employs Hubble-normalized scale-invariant variables
which are defined within the orthonormal frame formalism, and leads to the
formulation of Einstein's field equations with a perfect fluid matter source as
an autonomous system of evolution equations and constraints. This framework
incorporates spatially homogeneous dynamics in a natural way as a special case,
thereby placing earlier work on spatially homogeneous cosmology in a broader
context, and allows us to draw on experience gained in that field using
dynamical systems methods. One of our goals is to provide a precise formulation
of the approach to the spacelike initial singularity in cosmological models,
described heuristically by Belinski\v{\i}, Khalatnikov and Lifshitz.
Specifically, we construct an invariant set which we conjecture forms the local
past attractor for the evolution equations. We anticipate that this new
formulation will provide the basis for proving rigorous theorems concerning the
asymptotic behavior of spatially inhomogeneous cosmological models.
