Ion optical systems are used for the production of focused ion beams that find application in different areas of modern electronic technology. The proposed research is directed towards the development of a systematic procedure for the design of ion optical systems. The problem is being attached from two different directions: synthesis of ion beam systems from given elements, and synthesis of ion beam systems in their entirety. Ion optical systems are used in many different areas of science and technology, e.g. Electrical Engineering, Materials Science, Scientific Instrumentation, Biology, Physics, etc. Interdisciplinary basic research is proposed herein with the objective of the development of a general methodology for the design of complex ion beam systems.