Suggestion for a good book that explain Cartan's Moving Frame and Riemannian Geometry

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I'm studying Riemannian Geometry, and I'm having a lot of trouble with the books Riemannian Geometry and Differential Forms, both from do Carmo.

What book(s) would you suggest? I would also like the book to have examples and calculations, and (if possible) applications to physics. Thank you!