TITLE: Books to read before learning representation theory?
QUESTION [8 upvotes]: Next term I am taking a course in Representation theory, and have bought the book 'Representation Theory - A First Course' by Fulton and Harris. I am from a physics rather then maths background and as it stands there are many topics that Fulton and Harris assume knowledge of that I simply don't know. These include things like:

Exterior product
Canonical isomorphisms 
etc.

I am looking for a text book (ideally containing problems) that would enable me to learn this background information. I have tried looking in books on e.g. vector spaces or abstract algebra but these don't seem to cover all the areas I am looking for. Any ideas?

REPLY [7 votes]: I think that all the prerequisites for Representation Theory by Fulton & Harris are contained in the book Abstract Algebra by Dummit & Foote. In fact, Chapter 18 of this latter book is even an introduction into representation theory and the theory of characters. 
The book by Dummit & Foote is rather comprehensive so working through the entire book is definitely too ambitious. However, I really think that browsing through the relevant parts (and working through some of the exercises) should be sufficient.