Galois Theory, Third Edition

Rating:
Summary: Textbook plus Popularisation
Review: A lovely book that takes time to show off the applications of Galois theory. The expanded sections in the second edition really make a beautiful job of giving a historical and mathematically meaningful context to the central concepts.

However the main body of the work is a quite traditional textbook account that explorers the abstract idea of Galois groups over general fields - leaving the reader to inject the meaning and context. Someone, somewhere is capable of making the central concepts of Galois theory as natural and obvious to the reader as it was to Galois. But this isn't the book.

Rating:
Summary: Good, but SO many typos
Review: Good book, with a solid foundation in Galois Theory. Two major problems: the author introduces the theory over the complex field, when he really should start out in the abtract case. Worse, the book has many, many typos. They are all over the place. Someone really dropped the ball on corrections. So while this is a good intro, you need to constantly be on the look out for errors.

Rating:
Summary: Great Exposition of Galois Theory
Review: This is the book for Galois Theory. I've read most of the others and they go deeper into the formalization of the theory, but this book outlines it in an eminently readable format, with only the basics of Modern Algebra as a prereq. If you were to buy one book on Galois theory, this is the one (Tignol's book is a close second, but focuses more on the historical development of the theory).