Essence of this paper is to expand the results published concerning the primary aberrations of a thin lens. Starting with the contributions of the two refracting spherical surface, we have added the effects of considering each one as a rotationally symmetric polynomial asphere. As previous studies, we have worked with the bending variable (B) and the conjugate variable (C). In addition, two different media surround the lens and it has not the aperture stop in contact in order to get the effect of the aspherical surfaces on off-axis aberrations. As a result, the Seidel aberrations are third order polynomials in the variables B and C, except for the field curvature and chromatic aberrations, which preserve their form as they are obtained for spherical surfaces. The expressions can be used to incorporate the increase use of these surfaces in the predesign of not only simple but complex optical systems too, even to model axial GRIN lenses as it has been proposed recently. Moreover, modern algebra systems can make use of them to get an initial design for further optimisation.