A warning, though: trying to switch from a mathematician's idea of Lie groups and algebras to a physicist's, or anyone else's, is not easy. I am a mathematician with a research specialty in Lie groups, and I remember being asked a question about this paper—I can't remember what it was, or I would be more specific—a while ago that was mathematically easy to answer, but where most of the time it took me to answer was spent in decoding the notation.

This treatment is closer to the mathematician's than to the physicist's, but it still has some of the physics flavor about it—for example, it at least implicitly discusses Lie groups as if they come with a preferred action, which they need not—and, if you're not in this domain already, it's good to know what difficulties you can face later if you try to move between domains.