Complex Semisimple Lie Algebras

These notes, already well known in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers, including the classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and representation theory. The last chapter discusses the connection between complex Lie algebras and compact Lie groups, and is intended to guide the reader towards further study.