A book like this has been long overdue. There are Rovelli's and Thiemann's books of course, and there is Kiefer's book too, but to read one of these you have to make a major commitment, both in terms of time and in terms of finances.
Gambini and Pullin's book in contrast is a masterwork of omission, and as every science blogger knows that's a very under-appreciated art. The book comes at an affordable US$ 45.99 which, for a hardcover textbook really isn't much.
You need to bring only basic knowledge to benefit from the book. It starts very slowly, with special relativity and electromagnetism, goes on to general relativity, Yang Mills theory and quantum field theory. That is about the first half of the book. The rest of the book then deals with the reformulation of general relativity in terms of Ashtekar's variables, the quantization, loop representation, loop quantum cosmology and black holes, and a word or two on spin foams and the problem of time.
I think this book will be very useful for every undergraduate student who considers to work on quantum gravity and wants to know some more about the topic. Needless to say, the brevity comes at a price. That is that many intricate points are covered only very superficially and the reader is referred to the literature. If you really want to know all the details, this is not the right book for you. But if you want to find out if you want to know the details, this is the place to start.
Notably, the book finishes with a chapter on open issues and controversies, stating clearly and honestly that "Loop Quantum Gravity is an incomplete theory. We do not know if the current formulation... really describes nature or not." But, Gambini and Pullin add, "[I]t is refreshing that in loop quantum gravity there are not many things that can be tweaked to make the theory agree with experiment... This is in contrast to string theory, where the theory has evolved considerably over time and is now perceived by some as having too much freedom to be a predictive theory."
You can also read there
"In this modern day and age a lot of the disagreements about loop quantum gravity are aired in blogs and discussion groups on the Internet. In general we do not recommend people learn from the controversy there. Because blogs and Internet discussion groups are unedited opinions of people, some of which have questionable training or knowledge of the details, and are usually written relatively quickly, in many circumstances they contain highly inaccurate statements."
With that note of caution, in this relatively quickly written and unedited blogpost, I recommend Gambini and Pullin's book if you want to know more about Loop Quantum Gravity without getting drowned in details.
Gloria also liked it.