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What kind of recommendations do you have for a very good source to learn Galois Theory? Is there any Atiyah-MacDonald-type book on Galois theory? What is your opinion on the chapters from Lang and Dummit and Foote?

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  • $\begingroup$ I like Lang's presentation and learned the material from there, but he more or less copied it from Artin's lectures, if memory serves. $\endgroup$ – TTS Jul 11 '13 at 16:42
  • $\begingroup$ Artin's lectures are a great primer. TTS linked to a pdf, but the notes have been Dovered so you can get them cheap from Amazon (I got mine for <$10 IIRC). For a little more depth and some more applications/calculations (esp to number fields) Weintraub has a great book. $\endgroup$ – Ragib Zaman Jul 11 '13 at 16:51
  • $\begingroup$ I second Lang. While a lot of his book is crap from a pedagogical perspective the Galois Theory chapters are an exception to that. $\endgroup$ – Jim Jul 11 '13 at 17:13
  • $\begingroup$ @RagibZaman: I already placed an order for that, thanks :) $\endgroup$ – Manos Jul 11 '13 at 18:03
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    $\begingroup$ I never see this recommended: A Course in Galois Theory by D.J.H Garling. His exposition has been compared to G.H. Hardy. One of the best books for learning Galois theory. $\endgroup$ – Islands Jul 18 '13 at 16:07
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I really enjoyed learning Galois theory from Martin Isaacs' Algebra: A Graduate Course. Isaacs' textbook is a textbook on group theory, ring theory, and field theory (in other words, algebra!) so it's not just on Galois theory. However, you'll have a very complete knowledge of Galois theory if you read the latter half of the textbook where it is discussed. The textbook also has the distinct advantage of good, challenging exercises. The emphasis of the exercises in this textbook is on theory more than on specific computations and examples (although these are discussed as well; Isaacs generally feels, I suspect, that a student reading his textbook is already quite comfortable with specific examples and computations so should be able to do them independently). If you'd like to see worked computations and examples in detail, then perhaps it is a good idea to supplement Isaacs' textbook with textbooks like the one by Dummit and Foote on the same topic.

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  • $\begingroup$ Hello Amitesh. I was just looking at Dummit and Foote, and I found the section on Galois theory very good for a beginner (like myself). Do you know of any other textbook which handles Galois theory as such? Thank you! $\endgroup$ – Cauchy Aug 10 '17 at 6:56
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My suggestion would be Exploratory Galois Theory by John Swallow. This develops the basic theory that one would find in any course in abstract algebra, but from a very concrete perspective, so it seems easier to understand on a first read than other textbooks. See link

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Arnold has some lectures on Abel's theorem that you may find interesting. See Abel's Theorem in Problems and Solutions: Based on the lectures of Professor V.I. Arnold by V.B. Alekseev.

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