  We construct low regularity solutions of the vacuum Einstein constraint
equations. In particular, on 3-manifolds we obtain solutions with metrics in
$H^s\loc$ with $s>{3\over 2}$. The theory of maximal asymptotically Euclidean
solutions of the constraint equations descends completely the low regularity
setting. Moreover, every rough, maximal, asymptotically Euclidean solution can
be approximated in an appropriate topology by smooth solutions. These results
have application in an existence theorem for rough solutions of the Einstein
evolution equations.
