"Full details" Not bloody likely. Try Carter, Segal, and MacDonald, Lectures on Lie Groups and Lie Algebras for an overview and then Bump, Lie Groups for details on some of the most important ideas. You can find details on various approaches in many other books as well, such as Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications.
Caution: at any given moment, Wikipedia articles may be quite impressive or they may be terribly misleading and inaccurate. In particular, be aware that mathematical cranks exist and wikishilling is a problem in the math pages at WP.