I have done the equivalent of an undergraduate algebra course(rings/fields/groups) and have read Stewart's Galois theory book. Galois theory was a lot of fun and I would like to continue studying it but I have no idea how to progress studying it or what the big theorems/questions further are.
I would like any suggestions on books that extend basic galois theory. All the suggestions I can find are at the level of Stewart's book(ie. end with essentially a proof of the insolubility of the quintic).
You can try Theory of Commutative Fields By M. Nagata