TITLE: Learning representation theory of Lie groups for someone who knows Lie algebras
QUESTION [9 upvotes]: I'd like to learn the representation theory of Lie groups. I have a good knowledge of semisimple Lie algebras and their representation theory as well as the basics of Lie groups.
To what extent are the representation theories of the groups and the corresponding algebras interrelated? 
Is there a book you would recommend for someone who knows a lot about Lie algebras representations, but has only rather basic knowledge of Lie groups?

REPLY [2 votes]: I would suggest Knapp, Lie groups beyond and introduction and Knapp, Representation theory of semisimple groups (an overview based on examples).
If needed for a very simple introduction on very basics fact about Lie Groups is Hall, Lie Groups, Lie Algebras, and Representations