The analytical theories may be classified into (a) the older, semi-empirical theories, in which the approximations are physically motivated and rather unsystematic; typical of these are the so-called Significant Structures and Hole theories; (b) the newer theories, which we will, rather arbitrarily, refer to as the fundamental theories; here the approximations are of a more mathematical character and more systematically introduced; the perturbation and variational theories exemplify this approach. In addition, there are the Corresponding States methods, which occupy an intermediate position, in that, while having some fundamental justification, they are generally applied in an empirical manner.