A focused ion beam (FIB) system is a combination of low aberration electrostatic lenses that can provide a high current density beam of charged particles. It has specific features for application to lithography and maskless processes. The electrostatic lenses employed in an ion beam system are of various types and may be used for focusing of charged particles under acceleration and/or deceleration conditions. Design of electrostatic lenses is one of the most important tasks in electron optics since, unlike the magnetic lenses, there are no universal design curves for them due to the large number of physical and geometrical parameters that affect their focal properties. Thus their design is achieved by the method of optimization where the aberration coefficients should be as small as possible. Optimization by analysis and synthesis are the two approaches that are usually practiced in lens design. In the present work optimization by synthesis (inverse problem procedure) has been taken into account. The electron optical properties have been determined from the axial potential distribution, which is approximated by the cubic spline function. Two cases of spline lenses are investigated; namely, the simplest nontrivial spline lens defined over two intervals and the spline lens model defined over more than two intervals. The former has been used to investigate the effect of the electrostatic potential ratio on the relative optical properties (such as working distance, focal length, and spherical and chromatic aberration coefficients) under zero and finite magnification conditions. The latter has been used by means of the dynamic programming technique as an optimization procedure to determine the design of various types of electrostatic lenses (such as einzel, immersion and multi-electrode lenses) with the lowest possible spherical aberration coefficient under given constraints. The optimization procedure has shown the possibility of obtaining a practical design of electrostatic lenses Tor operation under pre-assigned conditions to yield minimum aberrations. Thus it is made easy to synthesize any type of lenses by simply varying the given constraints. Computer programs in Fortran language have been written and used in the design and optimization of electrostatic lenses for the two spline models. Non-relativistic velocities and neglecting the space charge effects are the two main assumptions that have been taken into account throughout the work. The paraxial ray equation has been solved numerically by using the fourth-order Runge-Kutta method and the aberration integrals have been solved by means of Simpson rule. The actual electrodes profile which is determined from the equipotential surfaces has been constructed in two and three-dimensional diagrams for the various types of the suggested lenses. A focused ion beam system has been put forward for various electron optical applications which is composed of the electrostatic lenses determined in the present investigation. The suggested system has the advantage that it can be practically realized.