List of contributors; Part I. Introduction, Basic Theory and Examples: 1. Model-theoretic logics: background and aims J. Barwise; 2. Extended logics: the general framework H.-D. Ebbinghaus; 3. Characterizing logics J. Flum; Part II. Finitary Languages with Additional Quantifiers: 4. The quantifier 'there exist uncountably many' and some of its relatives M. Kaufmann; 5. Transfer theorems and their applications to logics J. H. Schmerl; 6. Other quantifiers: an overview D. Mundici; 7. Decidability and quantifier-elimination A. Baudisch, D. Seese, P. Tuschik and M. Weese; Part III. Infinitary Languages: 8. L¿1¿ and admissible fragments M. Nadel; 9. Larger infinitary languages M. A. Dickmann; 10. Game quantification Ph. G. Kolaitis; 11. Applications to algebra P. C. Ecklof; Part IV. Second-Order Logic: 12. Definable second-order quantifiers J. Baldwin; 13. Monadic second-order theories Y. Gurevich; Part V. Logics of Topology and Analysis: 14. Probability quantifiers H. J. Keisler; 15. Topological model theory M. Ziegler; 16. Borel structures and measure and category logics C. I. Steinhorn; Part VI. Advanced Topics in Abstract Model Theory: 17. Set-theoretic definability of logics J. Väänänen; 18. Compactness, embeddings and definability J. A. Makowsky; 19. Abstract equivalence relations J. A. Makowsky and D. Mundici; 20. Abstract embedding relations J. A. Makowsky; Bibliography D. S. Scott, D. C. McCarthy and J. F. Horty.