The manual sets forth questions of the theory of the function of several variables, its differential and integral calculus and the basis of field theory. Multiples, curvilinear and surface integrals are considered in detail. The theory of the complex variable function is given, which is based on the mathematical apparatus of the function of two variables. In addition, methods for solving linear partial differential equations, often found in engineering practice, are considered. The content of the manual is set out in accordance with the course of higher mathematics for technical universities with a total volume of 450-510 academic hours.