In this paper we present a method of fnding eigenvalue and eigenfunctionrnfor linear second order elliptic dierential equation using the Fourier method.rnThen we present more specically for one dimension space called sturmliovillernproblems. Next Green's function to represent solution for sturmliovillernproblem and its properties.Finally we present reduction of the Sturm-rnLiouville Problem to an Integral Equation and properties of sturm-liovillernproblem