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Hello I wish to study Galois theory independently. I have no previous exposure to Galois theory specifically and was wondering if anyone had any tips or recommendations of good material I can use to do this (preferably online).

I have taken a course in algebra that covered, Rings, Fields, Quotient Rings, Ideals, Homomorphisms/Isomorphisms, Group theory and some basic number theory. So I should have a decent foundation to start learning Galois theory.

I looked online for some video lectures but it seemed quite sparse to be honest so it seems like using a textbook or online pdf would be the way to go but I need something approachable and that explains a lot rather than relying on results (I may not have).

Anyway thanks for looking and if anyone has any suggestions or advice then I would strongly appreciate it.

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I would recommend 'abstract algebra' by Dummit and Foote. It is available online.

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  • $\begingroup$ Wow that looks good almost 1000 pages! Shall I try and run through the section on Galois theory in there then (is it stand-alone) or do I need to pick and choose from other areas of the book as well? $\endgroup$ – Ryan Shaw May 31 '16 at 9:31
  • $\begingroup$ Because you already know field theory, I think you could just start at the section on Galois theory. It is a magnificent book, covering the most important topics in algebra. I recommend reading other sections too. $\endgroup$ – M. Van May 31 '16 at 11:16

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