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Now I am trying to learning GR. I planned to try David Tong's lectures on GR first and then read Sean Carroll's book. But I am not sure this plan now. I got lost in chapter 2, introducint differential geometry, in David Tong's lectures. It throws a lot of concepts I have never seen without sufficient examples, especially topics about Lie derivatives.

If you are familiar with Tong's notes, could you give me some advice that should I try other's notes, or just start with Sean Carroll's book?

Thanks!