I am asking if there are some good or standard references for proof complexity theory? I didn't find references when I search in internet. Thanks!

$\begingroup$ Previously posted on math.SE (with no answers): Reference for proof complexity theory. $\endgroup$ – Martin Sleziak Sep 10 '17 at 15:42

$\begingroup$ Perhap you could expand on what you mean by "proof complexity theory"? In the meantime, maybe this earlier MO question is relevant: Deep theorems and long proofs. In particular, see Joel Hamkins' references there. $\endgroup$ – Joseph O'Rourke Sep 10 '17 at 15:53
These are three books that I know:
 Logical Foundations of Proof Complexity
 Bounded Arithmetic, Propositional Logic and Complexity Theory
 Logical Foundations of Mathematics and Computational Complexity, Proof complexity chapter
Also, I suggest you read the following papers:
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Update. Jan Krajíček wrote a new book on this topic recently. You can find the final manuscript of it here.