These lecture notes are written with the hope that the recent advances in the subject of almost periodic differential equations can become more accessible if the basic facts are collected in one place. It is well known that in Celestial Mechanics, almost periodic solutions and stable solutions are intimately related. In the same way, stable electronic circuits exhibit almost periodic behavior. A vast amount of research has been directed toward studying these phenomena. A great portion of the roughly five hundred items in our bibliography are dated after 1955.
These lecture notes are about almost periodic solution to ordinary differential equations. I spend the first four chapters on the theory of almost periodic functions. Included in those chapters is the skeleton of almost periodic theory. I have taken the tack of presenting only that material which is germane to the later chapters on differential equations. I include essentially no fact about almost periodic functions which is not used to prove something else. This is no virtue. It illustrates the depth of the thoery that is developed here.