  In this paper we review the extent to which one can use classical
distribution theory in describing solutions of Einstein's equations. We show
that there are a number of physically interesting cases which cannot be treated
using distribution theory but require a more general concept. We describe a
mathematical theory of nonlinear generalised functions based on Colombeau
algebras and show how this may be applied in general relativity. We end by
discussing the concept of singularity in general relativity and show that
certain solutions with weak singularities may be regarded as distributional
solutions of Einstein's equations.
