Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.

This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

"This long awaited book ... fills essential gaps in monographic literature on proof theory and prepares readers for volume 2 (to be published soon) containing a

Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.