A special place in the presentation of the material is occupied by a detailed explanation and analysis of the basic, fundamental concepts. In addition, much attention is paid to those issues that are directly related to the school course of mathematics. The textbook is intended for students of mathematical faculties of pedagogical higher educational institutions. It will also be useful to students who are in the areas of training included in the UGS: "Metematics and Mechanics," "Physics and Astronomy," "Physical and Technical Sciences and Technologies," other technical areas of training and specialties and everyone who is interested in a detailed and understandable course of mathematical analysis.