A Course in Model Theory. - An Introduction to Contemporary Mathematical Logic

This book, translated from the French, is an introduction to first-order model theory. The first six chapters are very basic: starting from scratch, they quickly reach the essential, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. The next chapter introduces logic via the study of the models of arithmetic, and the following chapter is a combinatorial toolbox preparing for the chapters on saturated and prime models. The last ten chapters form a rather complete, but nevertheless accessible, exposition of stability theory, which is the core of the subject.