This is an introductory chapter to Part II, dealing with basic properties, needed in later chapters, of integrals with respect to positive, signed, and complex measures. The main focus of Part II, the investigation of measures on topological spaces, is left to the next three chapters. While we will not yet equip the underlying set X with a topology in this chapter, we do assume here, to avoid trivialities, that the underlying set X is nonempty.