Reddit reviews Vector and Geometric Calculus

Geometric algebra sounds extremely interesting. I definitely have heard that it makes a lot of vector calculus more intuitive, and apparently the results come more naturally from the framework. Most people I talk to haven't heard about it, and I'm surprised to see it being so applicable to so many fields. Especially interesting was when they said the theory isn't exactly equivalent in GR, leading to different calculations. Kind of crazy to see that in GA, curved spacetime isn't a thing. I'm not sure how that would work, since isn't the big picture in GR about particles moving through geodesics in curved space?

As an undergrad, I would definitely love the possibility of taking a class on it. I've seen a book that introduces linear algebra and geometric algebra together, though I haven't really gone through it that much. The author even made a textbook to teach vector calculus and geometric calculus as a natural generalization. Maybe one day I'll sit down and go through it.

Late, but here are undergrad books on the subject: geometric algebra, geometric calculus.

A grad-type book that has both and their applications to physics would be this one

I'm currently learning the geometric algebra undergrad book. It's a good read so far, and the author keeps up with book errors.