I've briefly heard of affine transformations in both linear algebra and calculus and I'd like to find a good book on the subject to study over the summer. So what's a good undergrad-level book on affine algebra (is that a thing or is it affine geometry?)?
In case it's germane, I've taken the calculus sequence, linear algebra, ODEs, a class on proofs, and an introductory real analysis course.
A classic text is Marcel Berger's Geometry, although it jumps right into group actions in chapter 1 and uses them to define affine spaces. I'm not sure how suitable it will be without some abstract algebra/group theory exposure, which you haven't listed.
Having studied linear algebra, you're already familiar with a very special family of groups, the group $GL(V)$ of invertible linear transformations from a vector space $V$ to itself. Nevertheless, the generality of abstract groups may make the treatment hard to digest.
It may not be appropriate for now, but it would certainly be beneficial to get some experience with algebra if necessary and return to this book.