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I'm looking for a short, concise introduction to Galois Theory (but please don't assume I know anything about Galois Theory). I don't want a complete and "fat" Bourbaki-style book.

My main motivation is to be able to read this pdf about Galois Schemes : http://websites.math.leidenuniv.nl/algebra/GSchemes.pdf because it look very interesting especially the connection between Topology, Algebraic Geometry and Galois Theory.

I just know basic facts about fields, and I followed one semester of commutative algebra (in the book of Atiyah-MacDonalds).

Thanks in advance.

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3 Answers 3

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The concise classic is Galois Theory by Emil Artin.

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  • $\begingroup$ @Ihf: This is a little out of date now. I remember the "field" used in the book is not assumed to be commutative, for example. $\endgroup$
    – Bombyx mori
    Feb 24, 2015 at 2:15
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A more recent "concise introduction" is Ian Stewart's "Galois Theory". Very pleasant to read.

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  • $\begingroup$ That is clearly not concise. $\endgroup$
    – Alex M.
    Jan 12, 2016 at 17:50
  • $\begingroup$ Well, Galois theory is not an elementary matter. Would you tsay that Artin or Rotman are more concise ? $\endgroup$
    – nguyen quang do
    Jan 12, 2016 at 20:27
  • $\begingroup$ Artin's book is clearly more concise, so are the first editions of "Classical Galois Theory" by Lisl Gaal - the most recent edition, though, has gained some weight. $\endgroup$
    – Alex M.
    Jan 12, 2016 at 21:26
  • $\begingroup$ @nguyenquangdo Can I ask you that how does Stewart vs. Rotman or Morandi? Thanks. $\endgroup$
    – Eric
    Jan 17, 2018 at 15:34
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A very good one is Galois Theory by J.Rotman. There is a very good introduction at the beginning of fields and rings, a very detailed appendix about the group theory, and a very good introduction to Galois Groupe et Galois theorem.

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  • $\begingroup$ I know the books by Artin, Rotman and Stewart. I prefer Stewart's, which I find easy and pleasant to read, and I have even used it to teach a course in Galois theory. I don't understand the reproach "not concise" from Alex M. because, as I said, after all, Galois theory is not an elementary matter. The most concise introduction I know is chapter 1 of Kaplansky's "Fields and Rings". But conciseness is not necessarily good for beginners. $\endgroup$
    – nguyen quang do
    Jan 17, 2018 at 20:21

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