There is a vast collection of available resources for learning GR. These are some that I have found the most helpful.
This, in my opinion, is the best textbook for learning GR. I know others love MTW, but I find it slightly dated and tough going. The Carrol textbook, conversely, is clear, intuitive and all the other positive adjectives. Free notes are also available, but the book is well worth buying. Carrol takes a ‘maths first’ approach, starting by outlining tensor algebra, manifolds etc. and not getting to ‘actual GR’ until Chapter 4. Whilst this can feel frustrating for those wanting to dive straight in, developing the mathematical machinery early is a worthwhile investment.
All though the title and front cover speak to the contrary, this is actually a serious book that does a good job at explaining things in a more condensed form than Carrol. Think of as ‘Carrol Lite’.
You can’t go wrong with this book, although the more modern Carrol is better IMO.
The classic GR bible. For learning GR, Carrol is better, but this is still a great resource and by virtue of being such a massive text, contains some topics excluded from Carrol (e.g. geometric optics in curved spacetime).
In addition to the above books, there are also some very good GR notes freely availbale on the web, easily found with Google. Some of the best are,