I'm going to start self-studying General Relativity from Sean Caroll's Spacetime and Geometry: An Introduction to General Relativity. I'd like to have a textbook on Differential Geometry/Calculus on Manifolds for me on the side.
I do like mathematical rigor, and I'd like a textbook that focuses on this aspect. Having said that, I'm ideally looking for a textbook that won't keep me densely involved with it; rather a textbook that I could hopefully juggle with the textbook on GR as well.
I looked for example at Lee's textbook but it seemed too advanced. I have done courses on Single and Multivariable Calculus, Linear Algebra, Analysis I and II and Topology but I'm not sure what book would be the most useful for me given that I have a knack of seeing all results formally.
Note: I am a student of physics with a mathematical leaning.
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