This lecture course is intended for students studying higher mathematics in various educational institutions. The book contains the necessary material on all sections of the higher mathematics course (linear and vector algebra, analytical geometry, fundamentals of mathematical analysis), which are usually studied by students in the first and second years of the university, as well as additional chapters necessary for studying special courses (double, triple, curvilinear and surface integrals, differential equations, elements of field theory and theory of functions of a complex variable, foundations of operational calculus). An accessible but scientifically rigorous language of presentation, as well as a large number of examples and tasks, will allow students to effectively prepare for passing tests and exams.