 Classification theory has two related though fundamentally distinct aims: to classify the models of a theory (or to show that such a classification is impossible) by some relatively simple combinatorial invariants and to classify theories themselves by the presence or absence of some fundamental structures within their models.  With the second edition of Classification Theory, Shelah dropped the subtitle “And the number of non-isomorphic models” in order to emphasize the broader goals of the project. In general, a class of theories may be recognized as classification theoretically robust if it admits characterizations both in terms of cardinals and with respect to some absolute condition on formulae relative to the theory.  For example, by definition, a theory T in a language L is stable if there is some cardinal κ ≥ |L| so that for every model M of T of cardinality at most κ, the number of 1-types over M is at most κ.  Equivalently, a theory T is stable if no formula has the order property relative to T. That is, there is no L-formula φ(x;y) (where x and y may be tuples of variables) so that for each natural number n it is consistent with T that there be a1, …, an; b1, …, bn so that φ(ai,bj) holds just in case i ≤ j. 