I. Basic Concepts. - 1. Definitions and first examples. - 2. Ideals and homomorphisms. - 3. Solvable and nilpotent Lie algebras. - II. Semisimple Lie Algebras. - 4. Theorems of Lie and Cartan. - 5. Killing form. - 6. Complete reducibility of representations. - 7. Representations of sl (2 F). - 8. Root space decomposition. - III. Root Systems. - 9. Axiomatics. - 10. Simple roots and Weyl group. - 11. Classification. - 12. Construction of root systems and automorphisms. - 13. Abstract theory of weights. - IV. Isomorphism and Conjugacy Theorems. - 14. Isomorphism theorem. - 15. Cartan subalgebras. - 16. Conjugacy theorems. - V. Existence Theorem. - 17. Universal enveloping algebras. - 18. The simple algebras. - VI. Representation Theory. - 20. Weights and maximal vectors. - 21. Finite dimensional modules. - 22. Multiplicity formula. - 23. Characters. - 24. Formulas of Weyl Kostant and Steinberg. - VII. Chevalley Algebras and Groups. - 25. Chevalley basis of L. - 26. Kostant's Theorem. - 27. Admissible lattices. - References. - Afterword (1994). - Index of Terminology. - Index of Symbols. Language: English