this is a collective effort to hit the easy parts of LQG for anyone who has shown an interest in this approach to quantum gravity to add constructive input Lubos Motl has been a critic of LQG and has just published a clear presentation of it, plus made an important contribution to and he recommends a certain 7 page paper by Rovelli and Upadhya as "an efficient review of Loop Quantum Gravity". Only 7 pages plus a couple of appendices and it introduces the subject! they call it a LQG "primer". he also recommends Thiemann LivingReviews for "a more extensive" presentation. I looked at the Rovelli-Upadhya primer and was very impressed by the clarity and conciseness. I think it is really the best paper to begin with of all I have seen (except it is 1998 so it uses SU(2) instead of SO(3)) Rovelli-Upadhya: arXiv:gr-qc/9806079 And Motl himself is exceptionally clear and concise in style, so his recommending Rovelli-Upadhya as a way into the subject carries a lot of weight with me. Motl: arXiv:gr-qc/0212096 I dont take Motl's bad-mouthing LQG seriously because he is bright and obviously very interested all of a sudden in LQG and he knows why and he contributes a solid mathematical result. His actions speak louder than his heckling. Motl's paper is also quite short, only 26 pages in all, and if you read it you see immediately that we need to review some things about SO(3). So I am hoping this thread can do some of that, and also recap some of the stuff treated in the previous two LQG threads.