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Classification theory of elementary classes deals with first order(elementary) classes of structures (i.e. fixing a set T of first ordersentences, we investigate the class of models of T with the elementary submodelnotion). It tries to find dividing lines, prove their consequences, prove"structure theorems, positive theorems" on those in the "low side" (inparticular stable and superstable theories), and prove "non-structure,complexity theorems" on the "high side". It has started with categoricity andnumber of non-isomorphic models. It is probably recognized as the central partof model theory, however it will be even better to have such (non-trivial)theory for non-elementary classes. Note also that many classes of structuresconsidered in algebra are not first order; some families of such classes areclose to first order (say have kind of compactness). But here we shall dealwith a classification theory for the more general case without assumingknowledge of the first order case (and in most parts not assuming knowledge ofmodel theory at all).  The present paper includes an introduction to the forthcoming book onClassification Theory for Abstract Elementary Classes

Introduction to: classification theory for abstract elementary class