I'm taking a course on Lie Groups and the Representations. We are using the book: Representations of compact Lie Groups by Bröcker and Dieck, and I find it very unorganized and sometimes sloppy. Can anybody recommend a very clear and rigorous book, where it is not prove by example, "it is easily seen", etc. I have taking a course on manifolds and riemannian geometry so i'm not a complete novice in the field of differential geometry. I've been thinking about the book Compact Lie Groups by Sepanski, anybody got a comment on this book? Thanks in advance.