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What are some good books on field and Galois theory?

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    $\begingroup$ Good for whom? Please clarify what target audience you have in mind: someone who has never seen the topics before, someone looking for a further study after a first course, or a general reference? $\endgroup$
    – KConrad
    Dec 22, 2010 at 2:53
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    $\begingroup$ Voting to close- this is too general for a reference request. $\endgroup$ Dec 22, 2010 at 3:10
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    $\begingroup$ I strongly agree with KConrad and Daniel Moskovich. A reference request shouldn't simply be "What are references for X?" Without any extra information, you may as well just look at what is well-reviewed on amazon: amazon.com/s/… $\endgroup$ Dec 22, 2010 at 3:29
  • $\begingroup$ I do not agree that Amazon gives scholarly information on books. On the contrary, they even do not give the standard library information like the publication year. When writing references for nlab I find amazon ads useless in providing full information including publisher, existing editions, original reference if it is a translation and so on. $\endgroup$ Dec 22, 2010 at 13:00
  • $\begingroup$ My favorite book on Galois theory is Patrick Morandi's FIELD AND GALOIS THEORY. It's not only the most complete book I've seen on the subject,it's the most readable. Definitely worth having. $\endgroup$ Dec 22, 2010 at 15:52

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David Cox "Galois Theory" Wiley 2004 is my current favorite. Lots of interesting material and very nicely written.

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Galois Theory by Emil Artin is a nice treatment of the latter.

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Chapter 1.5 The Absolute Galois Group of a Finite Field Might be useful from Field Arithmetic by Fried and Jarden.

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