The book is primarily devoted to the theory of the Kurzweil–Stieltjes integral and its important applications in functional analysis and the theory of various kinds of generalized differential equations, including the dynamical equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.