The textbook contains a complete and systematic presentation of the material included in the federal component of the discipline "Algebra" of the State Educational Standards for the specialties "Cryptography" and "Computer Security" . Unlike traditional courses of higher algebra, studied at the mathematical faculties of universities, this course is characterized by an in-depth study of discrete algebraic objects: finite rings, fields, linear spaces, semi-groups of transformations, groups of substitutions. Volume I contains the basic concepts and theorems of modern algebra in the volume of the annual course of higher algebra for students of mathematical specialties of universities. Volume II, along with the traditional material for mathematical specialties , contains such important sections for information protection specialists, The Theory of Finite Fields , polynomials over finite fields, Substitution Groups , Definitions of Groups, linear recurrence sequences, etc.