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I am interested in studying Representation theory and learning more about its applications. I find that I learn best through going through examples and problems; however, I haven't been able to find a good source of questions and solutions for learning Representation theory. I have looked at notes from Stanford's, Harvard's, and MIT's courses on Representation theory, and courses from other universities. I have also looked through questions on this site about good texts for studying representation theory. But I haven't found any that have solution manuals. While I can find homework questions online, I can only occasionally find solutions, and the whole process doesn't feel very systematic. I would be grateful for any advice and suggestions on website to look at/books to buy.

To give some indication of the level I am looking for, my university covers the beginnings of representation theory in its undergraduate Abstract Algebra sequence (which uses Dummit and Foote), which I have taken. It also has a dedicated Representation theory class. However, this class is pretty high level, and not easily accessible to students who have only taken the Abstract Algebra sequence.

Sorry if this question is not specific enough; I am new to StackExchange.

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    I would advice to read the first chapter of Serre's book. This is pretty elementary and quite efficient for understand the fundamental concepts. – 2017-02-18
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    Thanks for the suggestion! I read the first chapter of Serre's book; the material it went over was similar to the material in Dummit and Foote. – 2017-02-24
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    Ok. If you want more material, you have the book of Fulton and Harris, Representation theory : a first course. This is meant for representation of Lie algebras but they have good stuff about symmetric groups + finite matrices groups. Or you can try to read more of Serre :) (But I think material becomes more complicated after. ) – 2017-02-24
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    Liebeck's book is very good, I think. – 2017-02-24

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