am 20. Februar 2000
This book is one of the very best that Dover has out there. In my opinion, it is the ultimate book on Galois theory. All treatments written since this one were based on it, and do not add anything fundamentally new. There are only two things about this book which one could potentially complain about: 1) The awful cover. 2) There are no exercises because the book is just based on lecture notes. But that's forgivable, because there is no other exposition this good of Galois theory.
One wonderful thing about this book is that it is entirely self-contained. It starts by proving the few basic results from linear algebra it needs, and then builds from there in a beautiful way until the fundamental theorems of Galois theory have been proven in a most transparent way. Then, in the appendix, not by Artin, a few results from group theory are proven, just enough for the classical applications to the solvability of the quintic.
Every proof in this book is very clear and I cannot imagine how one could improve on any of them.
ET Bell claimed in one of his books that anyone who knew high school algebra could easily understand Galois's proof of the unsolvability of the quintic. I didn't believe that until I saw this book, which proves that ET Bell was absolutely correct.
am 14. August 2006
A very short introduction to Galois Theory. But for that little money you can't expect a real in-depth discussion of such a big theory. The basic theorems are very clearly written, the proofs are marvellous compared to any other book that I've seen on this topic. So, if you're looking for a little introduction, this is your book to get.
The layout of the text is a little old-school, because it's a reprint from the 1940's. There's sadly nothing like the modern TeX-style layout that you get in more recent math-books. But the quality of the text and the clarity of all the proofs make this book a definite good buy.