>>12870948>The professor will use Ian Stewart's book, is it any good?it's pretty good, although i believe there are better ones
>What do I need to know before learning Galois Theory?i assume you've had the standard groups-rings-fields sequence? you don't need anything beyond that. if you want to be more specific, you should know the rudiments of groups (group arithmetic, homomorphisms, normal subgroups, quotient groups and cyclic groups), what a field is, the properties of polynomials over fields (division, roots and irreducibility) and quotient rings (root adjoinment), that's about it (for basic Galois theory, for more advanced stuff you'd need more, obviously). as i recall Stewart covers the things i mentioned in the beginning (except for groups, i think)
my recommendation is check out pic related. this gives a VERY elementary introduction, i.e. it assumes pretty much 0 knowledge, but develops everything you need in 200 pages, including the proof of the unsolvability of the quintic. and, of course, it's written by John Stillwell, who is one of the best living expositors of mathematics
oh, and check out Richard Borcherds on YT, he recently did a short Galois theory course, although if you're very new to algebra it might go over your head a little
https://www.youtube.com/playlist?list=PL8yHsr3EFj53Zxu3iRGMYL_89GDMvdkgt 
