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I am an undergrad. I have taken courses in algebraic number theory and have a basic idea about $p$-adic numbers. I have also read a little bit of infinite Galois theory. But I have no idea about modular forms and automorphic forms and Galois cohomology.

I want to study about Galois Representations. All the books I have seen have titles like [some topic] and Galois Representations, where some topic=modular forms or automorphic forms.

Is there any textbook or lecture notes which does not require automorphic forms or modular forms as a prerequisite (suited especially for beginners)?

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    $\begingroup$ You can try Diamond and Shurman's book "A First Course in Modular Forms". Galois rep-s are covered in the last chapter. If you find it hard, you can try Goldfeld and Hundley's "Automorphic Representations and L-Functions for the General Linear Group". Its two volumes look huge, but it's written in a really beginner-friendly way. The latter focuses on the automorphic side only, though. $\endgroup$
    – M.G.
    Commented Aug 8, 2016 at 15:51
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    $\begingroup$ If you read German, you can also try Anton Deitmar's "Automorphe Formen". AFAIK, no English translation of it exists yet. $\endgroup$
    – M.G.
    Commented Aug 8, 2016 at 16:01
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    $\begingroup$ Related: mathoverflow.net/questions/77278/… and mathoverflow.net/questions/103846/… $\endgroup$
    – GH from MO
    Commented Aug 9, 2016 at 0:31
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    $\begingroup$ The notes entitles Galois representations from Gabor Wiese (easily found online) are exactly what you are looking for. $\endgroup$
    – Olivier
    Commented Aug 9, 2016 at 2:33
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    $\begingroup$ @user31415: there is none. Their book focuses entirely on the automorphic side. I mentioned it because of the low prerequisites and it's easy to understand. In particular, automorphic forms are not a prerequisite, but the actual subject :-) $\endgroup$
    – M.G.
    Commented Aug 9, 2016 at 6:43

2 Answers 2

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Galois representations have to come from somewhere.

If you are not interested in learning about modular forms and automorphic forms at this point, the other best source of representations are elliptic curves. You can find a gentle introduction in Silverman's book "The Arithmetic of Elliptic Curves", particularly the chapter on Tate modules.

As an alternative, for a completely "algebraic number-theoretic" approach, you might want to learn about complex Galois representations and their Artin L-functions. This is covered for example of Neukirch's book on ANT [Chapter VII] or Lang's [Chapters VIII and XII]. There's a lot of interesting and accesible number theory around it. That said, this alone won't get you too far in the way of understanding the big picture of Galois representations.

A nice general overview which doesn't jump directly into automorphicity issues is Richard Taylor's survey "Galois Representations", but it gets technical very quick.

You also might want to keep in mind the more advanced references in Emerton's great answer to this question.

There's also plenty of introductory text to modular forms. "A First Course in Modular Forms" has alredy been mentioned in the comments. The classic "A Course in Arithmetic" by Serre is probably the best general textbook on number theory that covers the basic of modular forms.

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You can see the book of J.P.Serre "Abelian l-adic representations and elliptic curves" a very nice presentation of Galois representations and properties !

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