A unified, coherent account of the algebraic aspects and uses of the Ziegler spectrum.

Mike Prest is Professor of Pure Mathematics at the University of Manchester.

Preface; Introduction; Part I. Modules: 1. Pp conditions; 2. Purity; 3. Pp pairs and definable subcategories; 4. Pp-types and pure-injectivity; 5. The Ziegler spectrum; 6. Rings of definable scalars; 7. m-dimension and width; 8. Examples; 9. Ideals in mod-R; A. Model theory; Part II. Functors: 10. Finitely presented functors; 11. Serre subcategories and localisation; 12. The Ziegler spectrum and injective functors; 13. Dimensions; 14. The Zariski spectrum and the sheaf of definable scalars; 15. Artin algebras; 16. Finitely accessible and presentable additive categories; 17. Spectra of triangulated categories; B. Languages for definable categories; C. A model theory/functor category dictionary; Part III. Definable categories: 18. Definable categories and interpretation functors; D. Model theory of modules: an update; E. Glossary; Main examples; Bibliography; Index.