  This is the first in a series Of papers in which we initiate the study Of
very rough solutions to the initial value problem for the Einstein Vacuum
equations expressed relative to wave coordinates. By very rough we mean
solutions which cannot be constructed by the classical techniques Of energy
estimates and Sobolev inequalities. Following our previous work on quasilinear
wave equations we develop new analytic methods based on Strichartz type
inequalities which results in a gain of half a derivative relative to the
classical result. Thus our result requires only $H^{2+\epsilon}$ regularity for
the data.
  Our methods blend paradifferential techniques with a geometric approach to
the derivation of decay estimates. The latter allows us to take full advantage
of the specific structure of the Einstein equations.
