Goa, Mengistu (PhD)Girma, Bizuneh2018-07-122023-11-042018-07-122023-11-042012-11http://etd.aau.edu.et/handle/123456789/8203This project contains two parts; theory of distribution and Sobolev spaces. In this project, we discussed theory of distribution and also the differentiations of distribution, multiplication by smooth function of distribution, direct product of distribution, convolution of distribution and the Fourier transform of function of slow growth. The theory of Sobolev spaces has been originated by Russians mathematician S.L.Sobolev around 1938. These spaces were not introduced for some theoretical purposes, but for the need of the theory of partial differential equationsenOn Distribution Theory and Sobolev SpaceThesis