The textbook corresponds to the state educational standard of the discipline ''Mathematical logic and theory of algorithms'' of the direction of training of certified specialists 654600 - ''Computer Science and Computer Engineering'' (Specialty 220100 -'Computers, Complexes, Systems and Networks') and the directions of bachelor's training 552800 - ''Computer Science and Computer Engineering''. The manual outlines the sections of mathematical logic and algorithm theory necessary for mastering general professional and special disciplines of the specialty 220100. The basics of sentence logic and predicate logic are described in sufficient detail, including the application of predicate logic to the proof of the correctness of algorithms. The manual contains introductory material on logical programming and clausal logic, as well as the basic concepts of fuzzy and modal logic. The basics of algorithm theory and algorithmic solvability, proof of equivalence of models of Turing algorithms and recursive schemes of Kline. are given. The allowance also contains:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------