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In this paper we review the extent to which one can use classicaldistribution theory in describing solutions of Einstein's equations. We showthat there are a number of physically interesting cases which cannot be treatedusing distribution theory but require a more general concept. We describe amathematical theory of nonlinear generalised functions based on Colombeaualgebras and show how this may be applied in general relativity. We end bydiscussing the concept of singularity in general relativity and show thatcertain solutions with weak singularities may be regarded as distributionalsolutions of Einstein's equations.Comment: Latex, 30 pages, final version, one reference added, to appear as  topical review in Class. Quantum Gra

The use of generalized functions and distributions in general relativity