This text is a draft textbook on mathematical analysis and the areas of mathematics on which it relies: mathematical logic and linear algebra (in volume, up to some deviations in the course of presentation, necessary to prove the statements of mathematical analysis). The idea that guided the author in his creation was to enable students and teachers to trace the chains of reasoning leading from the most elementary concepts of set theory to the main results of university mathematics. At the same time, the primary requirements for these chains were their clarity and continuity.