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Any particular suggestions? Although it is compact, I have tried to carefully choose the wording and arrange the sections so each concept builds on the last. Also, I intentionally avoid unnecessary mathematical abstraction; for example, the abstract definition of manifolds using coordinate charts, and tangent vectors as differential operators. This really tripped me up when trying to learn GR from standard textbooks.

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Maybe call it "The Mathematics of Relativity"?

It works well as an outline from my point of view, but I think you have to assume the reader already understands the Lagrangian in classical physics (which is a stretch for even the comparatively well-educated Hacker News audience). Also, somewhere around 3.5 it gets too dense with material I don't already know. (Christoffel symbols? Riemann curvature tensor?)

And then in the General Relativity section, there's simply too much material covered for any of it to be explained in depth beyond the necessary equations. I would drop the fluids (at a minimum) to give more space for other topics.

Needham's latest book might be a good source of intuition to "borrow" from for geometry.

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