Oh hey I'm actually posting about math and physics for once. Haven't done that in like a year huh.
I know with a title like that the book sounds intimidating but it really isn't. If you don't actively hate math and vaguely remember physics 21 (as usually taught at US universities) and even a smidge of 3d calculus2 you should go read it immediately. It is worth anything in between you'd need to learn/refresh on.
No other book starts at like, "so anyway here's a manifold, but for physicists" and then by a third of the way through just casually introduces the reader to how a wormhole would have to work before pivoting to knot theory. It's a fucking wild ride.
And the prose is so, so, so good. Baez is a great writer, possibly the greatest among living mathematicians who write for a technical audience. I came by this book by way of his work in category theory, and while this book decidedly doesn't touch on categories (he wouldn't get super into them until years after its publication), you can already see that sort of category-brained, "structure-forward" approach to mathematics all over the book.
I'm rereading it during my long-ass commute and have been blown away all over again. It's so, so fucking good. The exercises being sprinkled throughout the way they are makes it great for self-study, do them! They are essential and also mostly not that long!
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Or if you don't. It's like... helpful, but honestly you could get away with looking at things on wikipedia every couple hours
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If you really think you'd need a refresher first, go read the second best textbook of all time, Edwards' The Advanced Calculus of Several Variables. It's not an ordinary calculus text, it treats the underlying machinery with much more seriousness and rigor than that without fully falling into the weeds. You can honestly can stop right around where it starts talking about Forms, as that's where Gauge Fields, Knots, and Gravity picks up.