Abstarct: In this thesis, the shifted legendre polynomials are introduced and their properties are investigated. Then the Legendre wavelets is introduced and the operational matrix of derivatives for this wavelet is derived. The application of the proposed operational matrix for solving initial and boundary value problems is explained. Finally a numerical method for solving the Lane-Emden equations as singular initial value problems is presented. Using integral operator and convert Lane-Emden equations to integral equations and then applying Legendre Wavelet approximations. Illustrative examples are included to demonstrate the validity and applicability of the techniques. keywords :