'This book is in my view an excellent reference manual for a fundamental topic in mathematical logic and theoretical computer science.' Jaap van Oosten, Boekbesprekingen
Introduction; Part I. Basic Concepts: 1. Concepts and problems; 2. Frege systems; 3. Sequent calculus; 4. Quantified propositional calculus; 5. Resolution; 6. Algebraic and geometric proof systems; 7. Further proof systems; Part II. Upper Bounds: 8. Basic example of the correspondence between theories and proof systems; 9. Two worlds of bounded arithmetic; 10. Up to EF via the <...> translation; 11. Examples of upper bounds and p-simulations; 12. Beyond EF via the || ... || translation; Part III. Lower Bounds: 13. R and R-like proof systems; 14. _{d + 1/2} and combinatorial restrictions; 15. F_d and logical restrictions; 16. Algebraic and geometric proof systems; 17. Feasible interpolation: a framework; 18. Feasible interpolation: applications; Part IV. Beyond Bounds: 19. Hard tautologies; 20. Model theory and lower bounds; 21. Optimality; 22. The nature of proof complexity; Bibliography; Special symbols; Index.
