Believe it or not,the best quick introduction to Lie group and algebra theory I've seen is in chapter 12 of E.B.Vinberg's *A Course In Algebra*. Short,geometric and deep with all the essential facts and theorums 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 mostly drawn from the Vinberg/Onischick book mentioned by Victor above-but it's a little gentler and more 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 realize a little more just how damn **good** it is.