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: One of the major (classical) ingredients is the Szemeredi Regularity Lemma, which in itself is a really bizarre concept when you first come across it. On this subject, my favorite quick reference is:
http://www.ti.inf.ethz.ch/ew/lehre/GA10/lec-regularity-new-nopause.pdf
There's also Lovasz and Szegedy's "Szemeredi's Lemma for the Analyst:"
http://kam.mff.cuni.cz/~matousek/cla/lovasz-szegedy-continuousregularity.pdf
Also, in addition to Steven Stadnicki's reference, Tao also has the following set of notes:
http://terrytao.wordpress.com/2009/04/26/szemeredis-regularity-lemma-via-random-partitions/
A: The text Modern Graph Theory by Bollobas contains a chapter on extremal problems and Szemeredi's regularity lemma.  
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.  
