In this project paper we investigated solution for interior Dirichlet problem as mainrnparts. First, we showed uniqueness and continuity of Dirichlet problem in bounded regionrnusing maximum and minimum principle. Next, we transform the Laplace equation in tworndimensional Cartesian coordinate to Laplace equation in two dimensional polar coordinate.rnFinally, the Dirichlet problem in bounded domain using separation of variable and Fourierrnseries by appealing to annular region, rectangular region, heat equation and potential theoryrnwere discussed