Soft question: How does basic differential geometry "fit together"?

I'm self-studying diff geom from Lee's Introduction to Smooth Manifolds. He warns the reader that there's a lot of machinery to construct, which is fine, and he explains things with wonderful clarity. I couldn't wish for a better guide to the details.

But I feel like I could use a one-page overview of how these unfamiliar objects (manifolds, tensors, forms, Lie groups, frames, fibre bundles etc) fit together into a system; something to help me see the forest before I start prodding specific trees. I understand the basic definitions but lack a picture that shows how they fit together.

To re-iterate, I'm looking for an extremely high-level map only. Something I can print out and pin to my wall. Is such a thing possible? If it is, I feel sure someone must already have done it...


This is what I came up with after about ten minutes of doodling. As others have said, this will inevitably be missing things, but this is probably good to get you started. Note that my bias is mine, and does not necessarily reflect everyone else's views.

Also, note that "tangent spaces" was cut off at the bottom. It links to vector fields, distributions, frames, and Riemannian geometry.

Hand-drawn Overview of "The Basics"