  Hypersurfaces of arbitrary causal character embedded in a spacetime are
studied with the aim of extracting necessary and sufficient free data on the
submanifold suitable for reconstructing the spacetime metric and its first
derivative along the hypersurface. The constraint equations for hypersurfaces
of arbitrary causal character are then computed explicitly in terms of this
hypersurface data, thus providing a framework capable of unifying, and
extending, the standard constraint equations in the spacelike and in the
characteristic cases to the general situation. This may have interesting
applications in well-posedness problems more general than those already treated
in the literature. As a simple application of the constraint equations for
general hypersurfaces, we derive the field equations for shells of matter when
no restriction whatsoever on the causal character of the shell is imposed.
