1. Basic model theory and computability. - 1. Propositional logic. - 2. Deduction systems. - 3. First-order logic. - 4. Completeness of first order logic. - 5. Models of computation. - 6. Recursion and decidability. - 7. Incompleteness of Peano arithmetic. - 2. Descriptive Complexity. - 8 Complexity: time and space. - 9. First-order definability. - 10. Inductive definitions and second-order logic. - 11. Time complexity : the classes P and NP. - 12. Models of parallel computations. - 13. Space complexity: the classes L FL NL and PSPACE. - 14. Definability of optimization and counting problems. - 3. Approximation and classes beyond NP. - 15. Probabilistic Classes. - 16. Probabilistic verification. - 17. Approximation. - 18. Classes beyond NP. - List of Figures. Language: English