Differential Geometry, Lie Groups, and Symmetric Spaces

Description

Recommended here as a good introduction to Lie theory:

I would suggest you start with chapter 4 of An Introduction to Manifolds by Tu, Then study Lie Groups, Lie Algebras, and Representations: An Elementary Introduction by Hall and finally study Differential Geometry, Lie Groups, and Symmetric Spaces by Helgason.

In addition, someone recomended Stillwell's Naive Lie Theory as "a great first introduction".

also referenced in Whitman, S.J.'s Classical Theorems in Lie Algebra Representation Theory: A Beginner's Approach

Also in the bibliography of Gilmore 2008