The focus of this third volume of the introduction to analysis is on integral calculus for functions of several real variables. In addition, the book also includes introductions to the fields of complex analysis, functional analysis, Fourier analysis, distribution theory, and differential equations, particularly potential theory and boundary value problems. Due to its clear presentation, the book is well-suited both as a companion text for the lectures Analysis III and Analysis IV, as well as for self-study. Only the content from the introductory courses of the first year of study is required as prior knowledge.