The two sections of this chapter are rather different in nature.

The first section is a brief review of some basic model theory. Those who are already acquainted with this material will need only to glance at it for some conventions. On the other hand, those who know nothing of model theory may find that I have been too concise (although I hope not). The section does at least contain the essential definitions and results and I have tried to explain the main points. A number of texts may be recommended to the reader who desires more detail. The standard reference in model theory was, for some time, the book [CK73] of Chang and Keisler; the book [Sac72] by Sacks is quite readable, although less comprehensive. More specifically on model-theoretic algebra is Cherlin's [Che76]. All these are to be recommended, as are the very readable articles by Barwise, Keisler, and Eklof (and, relevant later, that of Macintyre) in the Handbook of Mathematical Logic [Bar77].

I would not recommend texts on logic in general, since these tend to begin with a very careful treatment of first order logic, which is tedious and probably off-putting to most mathematical readers.

The situation has changed recently, and I am now in the happy position of being able to recommend some more up-to-date texts which either have appeared or are soon to appear. In particular, as introductions (and a good deal more) to model theory, I recommend the books of Poizat [Poi85] and of Hodges [Hod8?]. The first of these also goes some distance into stability theory.