This book is an introduction to loop quantum gravity (LQG) focusing on its covariant formulation. The book has grown from a series of lectures given by Carlo Rovelli and Eugenio Bianchi at Perimeter Institute during April 2012 and a course given by Rovelli in Marseille in the winter of 2013. The book is introductory, and assumes only some basic knowledge of general relativity, quantum mechanics, and quantum field theory. It is simpler and far more readable than the loop quantum gravity text Quantum Gravity (Rovelli 2004), and the advanced and condensed “Zakopane lectures” (Rovelli 2011), but it covers, and in fact focuses on, the momentous advances in the covariant theory developed in the last few years, which have lead to finite transition amplitudes and were only foreshadowed in Rovelli (2004).
There is a rich literature on LQG, to which we refer for all the topics not covered in this book. On quantum gravity in general, Claus Kiefer has a recent general introduction Kiefer (2007). At the time of writing, Ashtekar and Petkov are editing a Springer Handbook of Spacetime, with numerous useful contributions, including that of John Engle's article on spinfoams.
A fine book with much useful background material is that of John Baez and Javier Munian (1994). See also Baez (1994b), with many ideas and a nice introduction to the subject. An undergraduate-level introduction to LQG is provided by Rodolfo Gambini and Jorge Pullin (Gambini and Pullin 2010).