The 4th edition of Ian Stewart's *Galois Theory* offers a terse but thoughtful introduction, I highly recommend it. Also, plenty of history is included if you're into that. As far as prerequisites go, a decent understanding of basic Ring theory will be helpful. Some of the first important technical results you encounter, namely Artin's extension Theorem and isomorphisms of splitting fields, are quite dependent on polynomial rings, their quotients, and ring homomorphisms. Knowledge of linear algebra, often of finite-dimensional vector spaces, is needed for building up field extensions. Lastly, I would suggest being comfortable with the idea of a group (the symmetric group in particular), normal subgroups, and the First Isomorphism Theorem for groups. I've found that some of the more niche group theory concepts, like solvability, are often introduced in tandem with Galois Theory making it quite digestible.
Galois Theory is a remarkable chunk of math, I'm excited for you. Enjoy!