This paper contains some of the main results about the theory of almost periodic complex valued functions of a real variable. We shall show an ap- plication to the theory of ordinary di erential equations: for an equation of the form dy dx = y +f(x); where  is complex constant and f is almost periodic function, we give a criterion of almost periodicity for bounded solutions (the existence of which is assumed) and other that ensure the existence of a unique almost periodic solution.