These are two books that I know:

 1. [Logical Foundations of Proof Complexity][1]
 2. [Bounded Arithmetic, Propositional Logic and Complexity Theory][2]
 3. [Logical Foundations of Mathematics and Computational Complexity][3], Proof complexity chapter

Also, I suggest you read the following papers:

 1. [The lengths of proofs][4]
 2. [Bounded Arithmetic and Propositional Proof Complexity][5]


  [1]: http://www.cambridge.org/us/academic/subjects/mathematics/logic-categories-and-sets/logical-foundations-proof-complexity#85v2LkjvjCOYq21Z.97
  [2]: http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521452058
  [3]: http://www.springer.com/gp/book/9783319001180
  [4]: http://www.math.cas.cz/~pudlak/length.pdf
  [5]: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiA7fH8_5rWAhWLPFAKHYuGALQQFggqMAA&url=https%3A%2F%2Fwww.math.ucsd.edu%2F~sbuss%2FResearchWeb%2Fmarktoberdorf95%2Fpaper.pdf&usg=AFQjCNHH5a_cOZekZvuoSGsx7eFTtnyGqQ