Reddit mentions of Vector Analysis (Undergraduate Texts in Mathematics)

I don't think you'll "spoil" what you'll learn later. If anything, seeing the material before will help you understand cooler stuff during the class next year. There's a lot of remarks and subtle examples I missed the first time I went through the standard undergrad math topics, that I only learned later.

But if you still want to avoid the topics you'll see in class, you could try some point-set topology (e.g. Munkres Topology). It would be beneficial for the real analysis class too. For differential geometry, I'd recommend Jänich Vector Analysis, which says it only needs calculus and linear algebra as prereqs.

Most of the books by John Stillwell, Klaus Jänich and John Conway. In particular, The Four Pillars of Geometry ,Numbers and Geometry, Vector Analysis, Topology