I would like to learn more about Cartan Geometry ("les espaces généralisés de Cartan"). I ordered Rick Sharpe's book "Differential Geometry: Cartan's generalization...", which would take a long time to arrive though. In the mean time, can someone recommend possibly some online lecture notes, or some online papers containing an introduction to Cartan Geometry, with I hope several examples worked out?
I kind of get what it is. When you model it on Euclidean geometry, it yields Riemannian Geometry. When you model it on affine space, it yields a manifold with an affine connection. When you model it on G/H, it gives a kind of curved space, which looks infinitesimally like G/H. Ok, this is the rough idea, but I would like to learn a bit more. Does anyone know of a few online resources on the topic by any chance?
Edit 1: I thank everyone who replied. I have learned a lot from various people, and I thank you all.
Edit 2: Check out the very nice and short introduction to Cartan geometry by Derek Wise (it is very well written and concise):
A hilarious point in the explanation, is the image of a hamster rolling inside a sphere tangent to the manifold (followed by expressions such as "hamster configurations" etc). It was really funny, and it explained the idea very well. I just realized that it is a shortened version of Derek Wise's thesis, which Tobias Fritz had already suggested as a reference in the comments below (thank you!).
Edit 3: R. Sharpe's book has arrived. I find it interesting that R. Sharpe's motivation for writing the book was this question "why is Differential Geometry the study of a connection on a principal bundle?". He wrote that he kept bugging differential geometers with this question, and that attempting to answer this question eventually led him to write his book on Cartan geometry! I appreciate anecdotes like this one.