The textbook is a modern introduction to linear algebra and analytical geometry for students of natural sciences faculties of universities. Basic algebra and geometry algorithms are presented in the Python programming language. In addition to the sections traditionally included in these courses, theoretical material and methods for solving practical problems in the theory of elliptic curves used in cryptography, as well as in the basics of quantum computing, are given. The content of the book corresponds to the GEF in the areas of training Information Systems and Technologies, Software Engineering, Information Security, Mathematics and Computer Science.