The book is a compact, easily understandable introduction to measure and integration theory, including probability theory. It also addresses the relationship to classical analysis, which is important for understanding, with sections on functions of bounded variation and the fundamental theorem of calculus. Despite its relatively small size, it covers all essential topics in these disciplines, such as set systems, set functions, measure extension, independence, Lebesgue-Stieltjes measure, distribution functions, measurable functions, random variables, integrals, expected value, convergence theorems, transformation theorems, product spaces, Fubini's theorem, decomposition theorems, functions of bounded variation, the fundamental theorem of calculus, Lp spaces, conditional expectations, laws of large numbers, ergodic theorems, martingales, and distributions.