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Although I am aware there are other questions asking for references of representation theory they are either too specific or too advanced.

I seek a text which is geared towards the beginning graduate student and not a particularly strong one at that. It should be noted that I am learning representation theory for the first time.

I would ideally like the text to be

-Accessible and no "magic" (No Rudin style "it's trivial" when it's not). Also nothing too advanced.

-Small number of pages between exercises (small being 10-15 pages) instead of a massive chapters with a few exercises at the end. Also a book with a lot of exercises is desirable.

-Hints or solution to exercises (big ask, I know)

-Less prerequisites is better

A good example of a textbook I really like in another discipline (measure theory) is real analysis for graduate students by Richard Bass, which you can see here. (although it has no solutions or hints)

http://bass.math.uconn.edu/real.html

I know that a book that satisfies all of the above is probably non existent and I do not expect references which have all of the above qualities. Any references that satisfy even only one of the above are greatly appreciated.

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I have been working my way through Gordon James and Martin Liebeck's Representation and Characters of Groups which offers a good intro to representation theory, and a review of groups. It is accessible and plainly written with lots of examples and straight forward exercises.

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  • $\begingroup$ Too character-heavy IMHO (a problem with many older texts). $\endgroup$ – darij grinberg Jun 26 '17 at 14:35
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Blake is probably right: Gordon James and Martin Liebeck's Representation and Characters of Groups is one of the first books you want to work out. Even if it has a kind of awkward notation on composition of functions, it is very readable and full of exercises.

Anyway as for a first approach I would suggest you chapter ten of Artin's Book, Algebra.If I remember correctly the chapter it should be titled "Group Representation" and it states all the basic notions in the simplest possible way. Read carefully that chapter, work out the exercises and then you'll have what you need to pass to all other books.

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These notes by Pavel Etingof et. al. cover a very broad range of material, and are not too difficult. They seem to be used frequently in reading courses etc., and are much more suited for self-study than, say, Fulton-Harris.

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  • $\begingroup$ A newer version was published as a book by AMS and is available from Etingof's website: www-math.mit.edu/~etingof/repb.pdf . That said, Etingof might be too much of a magic user by OP's standards (though Fulton-Harris is worse in that regard). $\endgroup$ – darij grinberg Jun 26 '17 at 15:09
  • $\begingroup$ I agree that it shouldn't be your first try. The book is really nice, full of interesting examples, but it is not at all didactic, is more a kind of "first approach to representation theory for smart guys" $\endgroup$ – Dac0 Jun 26 '17 at 18:31
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You can look at a book which I read when I first learnt Representation theory. It is called : Representation theory of finite groups-Benjamin Steinberg. It is written in a very simple way and as you said that the proof are given in detailed manner( without writing that it is trivial). A very striking feature of that book is that it doesn't use any kind of Module theory , that is, the theory semisimple modules, Artin Wedderburn theorem , tensor product of representations and all those things. But still it does a great job. Also it has a chapter on Representation of Symmetric groups which is also great.

But all being said you need know the module theoretic approach too. Group representation is a good book for that.

An advanced book with a lot of great exercises is "Character theory of finite group-I.M. Isaacs". It is a classic really. . I think you can give the book by Steinberg a try! I found it great.

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