Believe it or not,the
In my opinion, the best quick introduction to Lie group and algebra theory I've seen is in chapter 12 of E.B.Vinberg's E. B. Vinberg's A Course In Algebra. Short,geometric It is short, geometric and deep with all the essential facts and theorums theorems presented. There's a similar presentation in Artin's Algebra, but that one is done entirely in terms of matrix groups. The Vinberg chapter is on general Lie theory. By the way,it's way, it's mostly drawn from the Vinberg/Onischick book mentioned by Victor above-but above -- but it's a little gentler and more detailed,being detailed, being pitched at beginners.
The Vinberg book is one of those texts you read over and over because every time you look at it,you it, you realize a little more just how damn good it is.