Publisher Summary This chapter describes the equations when A is a (uniformly) almost periodic function of t; often, it is also assumed that f is almost periodic. The problems considered in this chapter are only to a small extent of periodic equations. Certain extensions to Stepanoff almost periodic functions (related to M as the uniformly almost periodic ones are to C) are possible to include all integrable periodic functions. The chapter also assumes that the essential results of the theory of (uniformly) almost periodic functions with values in a Banach space; this theory was developed by Bochner, and it closely parallels the case of realvalued functions. The chapter also considers the modules (additive subgroups) of real numbers, henceforth simply called “Modules” and denoted in general by German letters.