The manual is a course of lectures and is compiled in accordance with the requirements of the Federal State Educational Standard of Higher Education, the curriculum and the discipline program .. Contains the basic concepts of algorithm theory, questions of algorithmic unsolvability and analysis of algorithm complexity, construction and analysis of algorithms for sorting and searching information, as well as the basic techniques for solving various practical problems. It is intended for students of universities studying the discipline "Theory of Algorithms", studying in the direction of training 09. 03. 03 Applied Informatics .