IMO Axler's book should be read either during or after you take an introductory course on Linear Algebra.
> You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, this encounter will focus on abstract vector spaces and linear
maps.
Woah. That's a lot of books. Between the math, physics, and cs sections, years from now you'd look back and wonder if you really should have downloaded all of them.
https://www.math.brown.edu/~treil/papers/LADW/LADW.html