Subject of Research. The research results, structural composition analysis and the parametric synthesis of the projected imaging and non-imaging optical systems were presented. We made an attempt to use the gained experience about imaging systems while designing non-imaging systems, by adapting the composition theory for the calculations of non-imaging systems. Several patterns were revealed, which provide a deeper understanding of the design process of non-imaging optical systems; measures of its optimization were proposed. Method. We investigated the applicability of the theory of composition and synthesis of non-imaging optical systems. The main provisions of the theory of composition are based on the division of all available optical elements in four types depending on their functionality, which corresponds to a modular design. Similar items were identified in non-imaging optical systems and adaptation of composition theory to their design became possible. Main Results. General design patterns of imaging and non-imaging optical systems were studied. Classification of systems, components, as well as technical and generic characteristics of imaging and non-imaging optical systems was determined. Search mechanism of the initial optical system by means of structural and parametric synthesis of non-imaging optical system was formalized. The basic elements were determined included in non-imaging systems and their classification by functionality was done. They were subdivided into basic, corrective, wide angle and high aperture ones. The rules for formation of these elements and their composition were determined: surface reflecting, refracting, spherical and nonspherical elements with total internal reflection. The foundations of composition theory for non-imaging optical systems were laid. The approbation of this method was carried out on the example of the illumination system calculation for surgical room. A 3D model of an illumination optical system for surgical room was obtained, consisting of three identical domes. The illuminator designed with the use of the proposed methodology showed high energy efficiency (92.3%). Practical Relevance. The results can find application in optical design of non-imaging systems having various functionality, for example, illuminators, concentrators, etc. and can provide import substitution of similar foreign devices. The results can be useful by engineers specializing in the design and/or operation of non-imaging optical systems.