I assume that the reader knows what a module is: indeed, I take for granted a certain knowledge of basic module theory. The reader who does not have this or who needs his or her memory refreshed has a wide range of texts to choose from. On the other hand, I have tried to cater for the reader who has no idea what model theory is about. So, the first section of the first chapter is an introduction to the subject. I don't include any proofs there, but I do present the definitions and try to explain the ideas. That section ends with the formal statements of some results which I call on later. Despite the lack of proofs, the reader will not have to take too much on trust and will, in any case, see many of the ideas being developed within the specific context of modules. The second section of the first chapter introduces injective modules and may simply be referred as the need arises.

Chapters 2, 3 and 4 form the core of the book and provide a common foundation for the more specialised topics of later chapters. Especially in the second chapter, the pace is quite leisurely and there are many exercises and illustrative examples. The central result of Chapter 2 is the description of the definable subsets of a module (“pp-elimination of quantifiers”). Chapter 3 characterises modules of the various stability classes in terms of their definable subgroups. Hulls of elements and pp-types are the building blocks of pure-injective modules: they are introduced in the fourth chapter, together with a number of central ideas (irreducible pp-types, unlimited components, the space of indecomposable pure-injectives).