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The textbook consists of two parts. The first part deals with the theoretical foundations of algorithm construction, mathematical analysis, complexity and comparison, and their mathematical models, while the second part is devoted to the consideration and construction of more than 60 different normal and operator algorithms, sorting algorithms, algorithms on regular graphs, graphs and trees, information coding and compression algorithms, clustering algorithms, cryptographic and genetic algorithms. The operation of each algorithm is considered on a specific example to give the reader practical experience. The textbook is intended for undergraduate, graduate, and professional students who use relevant knowledge of algorithm theory and algorithms themselves.