Erdmann and Wildon Lie Algebras Ch5
Erdmann and Wildon’s Introduction to Lie Algebras covers eigenvalues, weights, and the Invariance Lemma.
Most of this information is inspired from Linear Algebra, and the topics of eigenvalues vs weights were rather confusing (in terms of a linear algebra background). However, the introduction of the Invariance Lemma (when applied to the broad range of Lie Algebras) was rather interesting. Below are my notes: