I want to learn about branching of representations in finite groups. In my field (chemistry) this is of certain relevance and I like to learn about what knowledge there is on the mathematical side. In practice I often encounter "dead ends" where I'd wish to have more knowledge, or at least the ability to communicate my problem to mathematicians.

My background is some basic abstract algebra, and a bit of very applied type representation theory as physicists and theoretical chemists learn it, which however does not extend much Schurs lemma.

So my first question would be, wherefrom to learn about the branching of representations in finite groups, best.

A second question would be how to approach modern representation theory best (what to learn in which order, which books). This is less of professional interest but more since I am fascinated by representation theory.

Maybe someone could also try to scetch what modern topics in representation theory cover and where to journey goes to?