I have a background in representation theory of the symmetric group and GL(n), and I need to learn quickly about representations of (semisimple) Lie algebras in order to follow a course I'm interested in. The books I'm using assume you don't know anything about representations. However, I feel I could be learning quicker if there was a book which more closely related both subjects, or maybe highlighted similarities and differences between the two theories. What sources would you recommend?
My suggestions are
B. Hall; Lie Groups, Lie Algebras, and Representations. It gives you a complete and simple introduction to Lie groups, Lie algebras etc. I would take this approach even if you do not immediately need the "Lie group" part and only the "Lie algebra" part since if you don't it's easy to get confused later on when you miss a lot of the motivations and the implications of some constructions.
K. Erdmann; Introduction to Lie Algebras. If you just want the "Lie algebra" part. You can't get a simpler introduction to Lie Algebra. There are also some YouTube lessons that follow step by step the book.