[...] The book consists of eight chapters that extensively cover the entire spectrum of differential and integral calculus of functions of multiple variables. Specifically, the first chapter introduces the reader to the basic elements of analytic geometry and topology, while the second and third chapters present the fundamental concepts of differential calculus of scalars and vector functions of multiple variables, such as partial derivatives, divergence, curl, and gradient operators, the Laplace operator, the Jacobian and Hessian determinants, as well as basic applications of these concepts, such as Taylor expansions, local extrema, applications in analytic geometry, etc. The remaining part of the book is dedicated to integral calculus of functions of multiple variables and analyzes, in order and through corresponding chapters, double, triple, generalized, line, and surface integrals, as well as the basic quantities and theorems related to them (flow and circulation of a vector field, Gauss and Stokes theorems). [...]

(from the author's preface)