The textbook includes a fairly complete and systematic presentation of the material in the "Algebra" section of the "Algebra and Geometry" discipline, which is part of the federal state educational standard of higher education (GEF HE) in the specialties "Information security of telecommunication systems," "Information security of automated systems" and "Information and analytical security systems." The main goal of the manual is to prepare a mathematical basis for reading, first of all, the discipline "Cryptographic methods of information protection," in which almost all sections of modern algebra are used. The manual pays special attention to the finite algebraic objects most in demand in cryptography - finite groups, rings and fields; polynomials and matrices over finite rings and fields, etc. Intended for students studying information security.