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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?

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