Discussions on the lack of a full theory of quantum gravity generally dwell on the incompatibility between quantum theory and general relativity. In his Lectures on Gravitation
Richard Feynman takes a different approach. He starts off by ignoring GR and trying to quantize the gravitational field, and then shows that his results match up with the geometrical theory of GR. The book benefits from Feynman's unique presentation - he explains the 'why' of choices made in physics and explores possible alternatives. It will be of particular interest to those readers wishing to get a background to the current arguments about theories of quantum gravity.
Note that this book is based on a course given for postdoctoral researchers, and is at a much higher level than Feynman's other Lectures. The first part (lectures 1 - 6) consists of some pretty technical quantum field theory, showing why the gravition has to be a spin 2 particle, and how this differs from other quantum fields. The second part (7 - 10) deals with Einstein's equations for general relativity. The last part (11 - 16) is somewhat simpler, looking at some of the applications of these equations. Unfortunately this part has largely been superceded, as it came just before the 'golden age' of general relativity.