The monograph is devoted to the method of the controllability function, which is a development of the method of the Lyapunov function on controllable systems. The application of the controllability function method to the problem of permissible control synthesis for different classes of systems of differential equations is given. Control is constructed in the form of function of phase coordinates, which satisfies specified restrictions, such that trajectories of closed system fall into specified end point in finite time. The results are illustrated by examples, figures.