The book consists of 18 chapters, divided into 3 parts: mathematical introduction, unitary classification of hadrons, mass formulas. The first part describes the main facts from the theory of complex linear spaces and structures above them, the main properties of groups, algebras and their representations. The statement gives the exact formulations of definitions and theorems, the proofs of theorems are usually omitted. This part includes numerous comments explaining the meaning and cause of the given results. The second part gives a detailed study of those particular groups (and their representations) that are needed to describe the symmetry of strong interactions, t. e. groups SU B), SU C), SU D) and SU F). In this part, attention is drawn to those aspects of the theory that are necessary for physics. The last part is devoted to the derivation of mass formulas, and it is more physical than mathematical. For mass formulas, a new rationale is proposed, allowing them to be interpreted more broadly. The bibliography contains the main works on the presented issue.