Whatever little bit of differential geometry I know, I've learned it mainly from these beautiful lectures by Prof. Fredrck Schuller. He covers differential geometry from an intrinsic viewpoint. He starts with a set and introduces more and more structures, until one could speak of Curvature of a connection on a Manifold.
He begins the subject from the very foundation of mathematcs: Logic. And then he goes on to explain the Zermelo-Fraenkel set theory, Topology, Topological manifolds, Differentiable Structure on Manifolds, Tensor space theory, Lie Group theory, Principal Fibre Bundles, Connections, Parallel Transport, Curvature and Torsion.
Check out this cool lecture series on importance of pictures in mathematics!
These are some interesting lectures on algebraic topology by Prof Tokieda.
In my opinion, Prof. Tokieda's enthusiastic lectures give insights into how mathematics is initially thought in terms of simple ideas and later translated into writing by adding rigour to it.
Kennington has a huge collection of references for differential geometry books. He has written a 2352 page book covering major aspects of differential geometry!
Checkout his site: http://www.geometry.org/