A computational investigation has been carried out in the field of non-relativistic charged-particle optics with the aid of numerical analysis methods, transfer matrices method, and personal computer under the absence of space charge effects. The work has been concentrated on the simulation of a transport and focusing ion optical system consisting of various types of electrostatic lenses operated under different modes and magnification conditions. The potential field distributions of einzel and immersion electrostatic lenses have been represented by analytic functions. The paraxial ray equation has been solved for the proposed fields to determine the trajectory of the charged particles traversing each lens. From the axial potential distribution and its first and second derivatives, the optical properties such as the focal length and the spherical and chromatic aberration coefficients have been computed. The electrodes shape of each electrostatic lens has been determined in two- and three-dimensions. An electrostatic quadrupole doublet lens has been also introduced to_ the transport and focusing system. The trajectory of the charged particles passing through it has been determined by using transfer matrices. The first-order optical properties of the quadrupole doublet are deduced from the elements of the matrices. Its spherical aberration coefficients are computed from those of the two single quadrupole lenses forming the doublet lens using the rectangular field model for the potential distribution. The proposed system consists of four electrostatic lenses for focusing an accelerated ion beam on a target. The first three lenses are rotationally symmetric, namely an einzel lens, an accelerating immersion lens, and a decelerating immersion lens; the fourth which is closest to the target is a quadrupole doublet lens. The optical performance of the whole system has been investigated. The results not only prove computationally the possibility of designing an electrostatic transport and focusing system but also show the possibility of constructing such system in practice.