Galois theory has been described to me by various people as, well, beautiful. It didn't really quite click that way with me, but the main result, that quintics and beyond don't have a general solution, rather neatly becomes kinda boringly obvious once all the heavyweight machinery has been created.
Instead, I found Galois theory a wonderful way of making other structures come to life. I learnt all about field extensions and finite fields, and things like that. Moreover, group theory stopped being tedious abstract theorems of little interest to me. As Galois theory is one of the birthplaces of group theory, it suddenly becomes clear what a soluble group is - it really is associated with the solvability of equations in a field and its associated Galois group. When a definition for a 'soluble group' is presented without explanation, things are not so fun.
So, that's the subject. What about the book? It treads a fine line between accessible specifics and abstract generalisation, and I think it does it well. I'm afraid I didn't read it in detail (it's my read-on-the-train book), so I skipped the exercises, and when the going got tough I skipped proofs. I'm a bad man. Having said that, it wasn't difficult to keep up for the first half of the book, and then the situation degraded gracefully. So, the presentation is good, and stands up to misuse!
It also makes me rather impressed with Ian Stewart. His pop maths books are ok, but show nothing of the depth of his knowledge. I rather enjoyed his Complex Analysis, but it didn't feel like it was really exercising him. Galois Theory tackles a much tougher and more abstract subject, and he handles it very well, including a good chunk of historical knowledge and insight into peripheral fields.
This is, I think, an early printing of the third edition, and the only thing that really lets it down is the huge set of printing errors, which sometimes make for rather confusing reading. Grrr. Otherwise, highly recommended.
Posted 2011-02-22.