In this work, a program of ray tracing program has been constructed. This program includes ray tracing for: 1. Skew ray tracing for spherical surfaces; 2. Skew ray tracing for Cartesian or quadric surfaces of revolution (conic surfaces). A study for the effect of asphericity factor (e) on the reflecting telescope parameters under investigation of this thesis has been accomplished by using the ray tracing code. These parameters are the ?-values (values for surface departure from the spherical), ray aberrations both the transverse (TA) and the longitudinal (LA), and the angle the incident ray makes with the surface normal vector. This study was useful to design a two-mirror reflecting telescope; it gave a suitable scope of understanding the problem sides, and provided a vision to minimize, directly, aberrations and consequently improving the optical system performance. Accomplishing this study demanded considering the bundle of incoming light rays as completely parallel to the optical axis; therefore, the design of the optical system is corrected for spherical aberrations only. The ray tracing code has been employed to exhibit the performance of the reflecting surfaces (mirrors) when the asphericity factor (e) is varying. Rays aberrations (transverse and longitudinal) aberrations have been considered as a measure to exhibit the performance of any conic reflecting surface (mirror) versus e. Aberrations reduction has been achieved through modifying, first, the secondary mirror radius of curvature and, second, the aspherisity factor (e) by using the principle of the Extreme-Value Theorem. The design of the telescope, achieved upon this study, is a two-mirror system of 2.5m focal length corrected for spherical aberrations; the primary mirror is paraboloid of 1m aperture and 5m radius of curvature and the secondary is hyperboloid of asphericity factor e = - 0.21. The considered light wavelength in the calculations concerning the telescope is 550nm because it is in the middle of visible spectrum of light.