I’m writting this post to keep track of books on quantum gravity (and closely related/helpful books). I own only the first one, which I recommend if you are interested in the main conceptual problems of quantum gravity. Regarding the others, I am presently considering purchasing Thiemann and Henneaux & Teitelboim’s books.
Rovelli – Quantum Gravity (errata)
Thiemann – Modern Canonical Quantum General Relativity
Kiefer – Quantum Gravity
Amelino-Camelia – Planck Scale Effects in Astrophysics and Cosmology
Gomberoff – Lectures on Quantum Gravity
Ambjørn et al. – Quantum Geometry: A Statistical Field Theory Approach
Carlip – Quantum Gravity in 2+1 Dimensions
Gambini & Pullin – Loops, Knots, Gauge Theories and Quantum Gravity
Henneaux & Teitelboim – Quantization of Gauge Systems
Rickles et al. – The Structural Foundations of Quantum Gravity
Callender – Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity
There is also Daniele Oriti’s book, which is an edition of several contributions about various approaches to quantum gravity. As it appears, the book has not been released yet. You can learn more about it over at my old blog, Background Independence (scroll down after my two book reviews to find Oriti’s invited post). At that blog you can also find my “Basic Curriculum for Quantum Gravity” (scroll down a little more, after Oriti’s post, or use this direct link to a backup copy of that post, with comments). There, I link to several other helpful books and downloadable tutorials/papers. That list have not been updated. I believe these two papers by Ashtekar are useful recent reviews:
There is also Smolin’s 2006 Lectures on quantum gravity. See here for more details.