This work deals with multi-element systems representing a set of interdependent identical elements of a comparatively small size. Such systems are widely used in various fields of astronomy and radio science, their classical examples being radio telescopes, optical and radio interferometers, orbital X-ray and gamma-ray telescopes, and phased antenna arrays for radio communication and radar facilities. Here, the problems of the optimal arrangement of elements of such systems are investigated to provide their high-performance characteristics such as resolution, sensitivity, and robustness to the statistically inhomogeneous propagation medium. The distinctive feature of the book is the use of the combinatorial approach to system optimization that proves especially useful for systems with a very large number of elements. The book is addressed to research physicists and engineers who are concerned with the development of astronomical instruments and large antenna arrays, and to graduate students learning about these subjects.