We studied that the transfer matrix ABCD theorem for the passage of paraxial rays or the optical system possessing a rotational symmetry axis can be generalized for the skew rays propagated off-axis, whether the optical system possessing rotational symmetry axis or not. We noticed that the same ABCD relation exists in the classical mechanics also. This fact hints samething more need to be considered. As a consequence, the connection of ABCD theorem with the fundamental " uncertainty principle " in quantum mechanics had been established. Furthermore we applied the general ABCD theorem to evaluate the diffraction integral, matrix elements A ~ D expressed in terms of the angular eikonal function T, and the primary aberration included. Finally the numerical results in the case of only spherical aberrations are presented.