Vector analysis traditionally deals with vector fields, the operators gradient, divergence, and curl, as well as line, surface, and volume integrals, and the integral theorems of Gauss, Stokes, and Green. In its modern form, it is the Cartan calculus with Stokes' theorem. This book fundamentally represents the modern approach but also carefully addresses classical notation and concepts. It is aimed at mathematics and physics students from the second year onward who are familiar with the basic concepts of differential and integral calculus in one and several variables, as well as topology. The author's very personal style and the familiar learning aids from other books, such as numerous figures, more than 50 commented exercises, and over 100 tests with answers, make this text excellent for self-study as well.