It may depend in part on how much background you retain. As a student I also never really learned Galois theory, and as a professor it always seemed to get squeezed out the end of the courses I taught and we never got there. So one year I resolved to teach Galois theory first, so I could learn it myself. That was not so easy as I realized there is so much background material, groups, linear algebra, ring and field theory. So I spent the first quarter mostly on group theory, then snuck in a little linear algebra (dimension theory and determinants), then finished up the first quarter by discussing finite field extensions, the concept of normal extensions, and finally at least defining a Galois group, and using it to prove that a solvable polynomial must have a solvable Galois group. That took about 125 pages of class notes. (843-1 and 843-2 on my webpage.)
the second quarter we looked at the converse result, that in characteristic zero, a polynomial with a solvable Galois group in fact has a solution formula by radicals, and we derived these formulas to some extent for cubics and quartics, with some errors in the case of quartics. Then we did some examples of calculations of Galois groups, and considered the inverse Galois problem: which finite groups occur as Galois groups, proving that all finite abelian groups do occur. The second quarter class notes occupied another 100+ pages. (844-1 and 844-2 on my webpage.)
This means that if you need to review the background algebra first, then do the Galois theory, and then also want to explore some of the applications, as I do in my notes, then at least my treatment of these topics took over 225 pages. My notes are free on my webpage, but unfortunately the quality of reproduction of the type fonts online has deteriorated over the decades since they were first posted, and they are a little troublesome to read now, but still readable with patience.
https://www.math.uga.edu/directory/people/roy-smith
I also did not understand the subject as well as the other authors referred to in previous posts here, but did my best to explain every detail to my class as well as I could. I.e. I read and tried to learn the material from the other more authoritative sources I cite, and then I tried to explain it in more detail than those sources did, which was my excuse for writing another book. I used and especially liked the book by Michael Artin, as opposed to the famous Notre Dame notes of his father Emil Artin, and would recommend Mike's book to almost anyone. It was written for sophomores at MIT. In fact if I had found Mike's book sooner, I might not have written my book. Our books do differ though since I include multilinear algebra in mine. I also happen to like Van der Waerden. Another book that is considered very user friendly is that of Ian Stewart. From the reviews on Amazon, I would suggest getting an older edition, e.g. from abebooks:
https://www.abebooks.com/servlet/Se...lts&an=ian+stewart&tn=galois+theory&kn=&isbn=
If you like the Bourbaki style, then chapter 5 of Bourbaki's Algebra, is devoted to a full discussion of the theory of commutative fields, including Galois theory, in about 120 pages. Here is a reasonably priced french copy:
https://www.abebooks.com/servlet/BookDetailsPL?bi=30222162639&searchurl=bi=0&ds=30&bx=off&sortby=17&tn=algebre&an=bourbaki&recentlyadded=all&cm_sp=snippet-_-srp1-_-title17the only english translation i found was offered at over $2,000, but with free shipping!
