Representation Theory: A First Course: 129 (Graduate Texts in Mathematics, 129)

Requires a VERY GOOD knowledge of Linear Algebra. The proofs in the book understand you are hugely familiar with advanced concepts in it.

I don't want to repeat what others have said in the (few) negative reviews, except that I generally agree with them. Despite what the authors claim, this is not a book that should be used as a first introduction. It is written in a chaotic way and the authors even forgot to actually define some crucial concepts. For example, they define the adjoint representation of the Lie algebra of a Lie group, but then they never define it for an abstract Lie algebra — even though they take for granted that one knows what it is. And they casually refer to the concept of a simple Lie group even though you'll be hard pressed to find its definition in the book.