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What are some good introductory books on Galois connections? I have read Galois Theory from Emil Artin, Algebra from Saunder Mac Lane, and I'm starting Serge Lang.

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    $\begingroup$ Do you mean Galois Theory or abstract Galois connections ? $\endgroup$ – lhf Apr 11 '11 at 11:11
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    $\begingroup$ I simultaneously feel that this is not a very good question and have a lot of sympathy for it. I have had occasion to wonder in recent years "Why isn't there a book on Galois Connections that takes the perspective I want?" Part of the problem being that I'm not really sure what perspective I want...but I'd probably know it if I saw it. $\endgroup$ – Pete L. Clark Apr 11 '11 at 15:25
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Steven Roman's book Field Theory treats the Galois Theory part of his book using Galois connections. I don't have the book but I had browsed through it one time when I was looking for a different book in my university library, and I have to say that it seemed pretty good.

In particular, take a look at chapter 6, where he develops some theory about Galois connections and applies it to study the Galois correspondence.

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George Bergman's Universal Algebra book has a chapter that discusses Galois connections (Chapter 5); the link is to the PDF version. I like it, though it's not very extensive (just six pages).

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