Jacobi modular forms constitute a bridge between arithmetic and different mathematical subjects like algebraic and geometry, topology, mathematical physics and string theory. The theory of Jacobi forms was stated by the great book of M. Eichler and D. Zagier (1985) which was cited a thousand times. We follow another way in the theory (in particular, our main hero is the odd Jacobi theta-series and we consider Jacobi modular forms in many variables) but we try to keep the style and the spirit of this wonderful book. The target audience of this online HSE course contains all master and post-graduate students in mathematics and physics. Basic knowledge: 1) Complex analysis (a very basic course); 2) The theory of quadratic forms (a very introductory course). 3) It is better to know the definition of modular forms with respect to the full modular group SL_2(Z). See the first part of the section 7 of J.-P. Serre «A Course in Arithmetic». In any case we discuss this definition in the course. After this distant course students will be able to start a realisation of their individual research project or master thesis in the theory of modular forms of many variables and their applications. The results of the theory of Jacobi forms of many variables have been presented so far only in scientific articles. The course will focus primarily on various applications of Jacobi forms and will be available to students specializing in various areas of mathematics. The course consists of 12 video lectures nearly for 90 minutes and 12 tasks with exercises and problems related to every lecture. All tasks will be evaluated. We are planning to prepare a book based on this online course.