Reference request: classification of simple Lie groups and simple real Lie algebras

Question

I am trying to understand the classification of simple Lie groups and the theory of highest weights for semisimple Lie groups by first understanding the case for complex Lie algebras, then relating to real Lie algebras, and finally to Lie groups. I've got the first part (on complex Lie algebras) down, but I am looking for some good references for the following:

1. Classifying the real forms of complex simple Lie algebras
2. Classifying which simple Lie groups correspond to a given simple Lie algebra
3. Developing a theory of highest weights for real semisimple Lie algebras and semisimple Lie groups.

For 3 I am guessing one compares real representations of a real form of a complex lie algebra $\mathfrak{g}$ to representations of $\mathfrak{g}$ and then compares representations of a Lie group to those of it's Lie algebra. Is this correct?

Answer 1

For n.2, as far as I know, such a classification has not yet been published explicitly anywhere. For such a classification, you need to know the centers of simple simply connected Lie groups (and this is known) and the actions of external automorphisms of such Lie groups on their centers (which, it seems to me, has not been written down explicitly by anyone, although all the necessary information for this is available). Surprisingly, it is a fact that such a classification has not yet been published by anyone, although it only requires perseverance and analysis of a fairly large number of special cases.