"General relativity" by Hobson, Efstathiou and Lasenby is a gem. When I bought it, I had already picked up several other books on general relativity (GR), but none of them really satisfied me. This book was the only one that left me feeling at ease with the physical principles and the mathematical apparatus of GR. Assuming only a basic knowledge of special relativity and vector calculus, it develops the theory in a way that is intuitive, accessible and enjoyable.
The mathematical background (tensor calculus, metrics, curvature etc.)is presented in a way that is extremely easy to visualize. It doesn't do the maths in the most rigorous way, but it does do it in the most intuitive way. That intuition is absolutely indispensible.
Once the mathematics is in place, the Einstein field equations are justified in a manner that is compelling and convincing - the equations almost end up feeling inevitable! The authors pay particular attention to how observers make measurements in GR; this is a crucial thing to understand, yet it is covered so poorly in many other books.
Finally, the authors go on to look at particular solutions of the field equations, including black holes, cosmology and gravity waves. They examine experimental and observational evidence as well as the theory. For exam purposes, this book is very helpful because it trains you to derive and solve equations of motion in almost an algorithmic way.
This book was a lifesaver for me - I highly recommend it.