The textbook contains a complete summary of the material of the academic disciplines "Mathematical Logic and Theory of Algorithms" and "Discrete Functions" of the State Educational Standard of Higher Professional Education in the specialties "Computer Security" , "Information security of automated systems" and some other related specialties. The manual consists of three interrelated parts, which, respectively, constitute the basis of mathematical logic, the theory of discrete functions and the theory of algorithms. It is intended for university students studying in the field of information security, as well as for graduate students and students of universities of other technical specialties studying discrete mathematics.