Q:

Books to understand Szemeredi's regularity lemma?

I want to understand the Szemeredi theorem and read on the thoery relating to it. Which books should I pick up to do this? Regards

A:

The question is not comlpetely clear to me in that I do not know if it asks maily/only about Szemerédi's Regularity Lemma (title) or at least also about Szemerédi's Theorem on arithmetic progressions (body), which are quite different things. 
(The former being somehow considered as a tool for the latter, and also it or variants of it can be used in this way, but historically this is not so clear; ideed Szemerédi says the regularity lemma has nothing much to do with the theorem, see an interview with Szemerédi, page 226, 2nd column at the start.) 
That being said: 
For the regularity lemma there are already several references given, I will add another graph theory book that contains it: 

Bondy and Murty, Graph Theory (Springer, Graduate Text in Mathematics 244)

For Szemerédi's Theorem I would receommend 

Tao and Vu, Additive Combinatorics (CUP)

This book contains in one of the last sections, I think the penultimate, a proof of it, and the preceeding section contains a proof of the special case progressions of lengt three.  

