This is a multipurpose text. When taken in full, including the “starred” sections, it is a graduate course covering differentiation on normed spaces and integration with respect to complex and vector-valued measures. The starred sections may be omitted without loss of continuity, however, for a junior or senior course. One also has the option of limiting all to En, or taking Riemann integration before Lebesgue theory (we call it the “limited approach”). The proofs and definitions are so chosen that they are as simple in the general case as in the more special cases. In a nutshell, the basic ideas of measure theory are given in Chapter 7, §§1 and 2. Not much more is needed for the “limited approach.”