L. State, reviews.com
"This most erudite of books will stand the test of time. I will revisit it often."
George Hacken, Computing Reviews
"... very great detail and with care... The presentation of the book is most thorough and the treatment rigorous, providing the reader with the right amount of intuition and detail to follow even complicated constructions. The new book by Cook and Nguyen will become another classic for the field of bounded arithmetic and its relations to computational complexity and propositional proof complexity. It will serve as a rich source of reference for the expert and as a thorough guide to the student interested in learning about this beautiful field."
Olaf Beyersdorff, Mathematical Reviews