> Great suggestions. I would add that Calculus on Manifolds might be sufficient for differential geometry. Maybe. I'm just going by how all of these were taugh

> Great suggestions. I would add that Calculus on Manifolds might be sufficient for differential geometry. Maybe. I'm just going by how all of these were taught during my undergrad. IIRC it doesn't cover metric spaces at all, but in fairness an introductory GR course will cover that; CoM will set up the mathematical context for you.