Good reference for Galois theory.

Question

I am a graduate student.I have a firm grasp on group and ring theory.Now I am learning Galois theory.But the problem with our instructor is that he is very clumsy and I am not finding motivation behind the theorems I am doing,like what the theorem really means,although I know the motivation behind this topic which is solvability of a polynomial by radicals.I started self studying as I was not satisfied with the teaching of our instructor.But the books also do not provide much insight and simply state and prove the theorems.Although I understand what the statement wants to say but I do not realize what the theorem really wants to say.In such situation I am badly stuck and cannot find a way out.I have to somehow learn this theory properly.I also referred to some lecture videos but none of them serve my purpose.I do not have clear idea about normal extensions,separable extensions and most importantly the Galois extensions.These things seem to me coming out of the blue.I do not even understand the meaning of Galois correspondence theorem.So,I need some reference where I can find both proofs and insight behind those proofs.I want to make a complete note so that I can refer to it while studying.Can someone help me?

Answer 1

The book Field Theory and Its Classical Problems by Charles Robert Hadlock emphasizes the classical motivation. https://bookstore.ams.org/car-19

https://www.jstor.org/stable/10.4169/j.ctt5hh8wp#:~:text=Field%20Theory%20and%20its%20Classical%20Problems%20lets%20Galois%20theory%20unfold,polynomial%20equations%20by%20radicals%2C%20and