Currently, most of what I know in algebra is contained in the first four chapters of Hungerford's Algebra, which covers basics of groups, rings and modules. For linear algebra, I've read Hoffman & Kunze, up to Jordan forms.

Since I know some group theory, I would like to read texts like Character Theory of Finite Groups by Isaacs, and Linear Representations of Finite Groups by Serre. But my interest is not limited to representation theory of finite groups only. I know there is, e.g., representation theory of algebras, which I also want to study, although presently I know nothing about algebras.

So what are the prerequisites for representation theory? By prerequisites I mean just everything (if that's possible to list) one might need for a thorough and detailed study of the subject. I'm in no hurry, so I plan to spend a lot of time preparing. I just don't know what to read. I've searched through the site but surprisingly, it seems that this question has not been asked yet.

Thanks for any advice!


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