Several of the books mentioned in other answers are devoted mostly or entirely to Lie algebras and their representations, rather than Lie groups. Here are more comments on the Lie group books that I am familiar with. If you aren't put off by a bit archaic notation and language, vol 1 of Chevalley's Lie groups is still good. I've taught a course using the 1st edition of Rossmann's book, and while I like his explicit approach, it was a real nightmare to use due to an unconscionable number of errors. In stark contrast with Complex semisimple Lie algebras by Serre, his Lie groups, just like Bourbaki's, is ultra dry. Knapp's Lie groups: beyond the introduction contains a wealth of material about semisimple groups, but it's definitely not a first course ("The main prerequisite is some degree of familiarity with elementary Lie theory", xvii), and unlike Procesi or Chevalley, the writing style is not crisp. An earlier and more focused book with similar goals is Goto and Grosshans, Semisimple Lie algebras (don't be fooled by the title, there are groups in there!).
The book "Introduction to Lie groups and Lie algebras" by A. Kirillov, Jr., is quite nice, and seems to be free online. It might be a good starting point, and it has an excellent annotated bibliography. (Edit: On further inspection, the .pdf I linked to just seems to be a draft. The actual book has the good bibliography.)
Bourbaki Lie Groups And Lie Algebras Chapters 13 Pdf 26
I like Humphreys' book, Introduction to Lie Algebras and Representation Theory, which is short and sweet, but doesn't really talk about Lie groups (just Lie algebras). I also sometimes find myself looking through Knapp's Lie Groups: Beyond an Introduction. If the material was covered in the Spring 2006 Lie groups course at Berkeley, then I prefer the presentation in this guy's notes. 2ff7e9595c