Lie groups and Lie algebras, part I (chapters 1-3)

Title
To the reader
Contents of the Elements of Mathematics series
Contents
I. Lie Algebras
§ 1. Definition of Lie algebras
§ 2. Enveloping algebra of a Lie algebra
§ 3. Representations
§ 4. Nilpotent Lie algebras
§ 5. Solvable Lie algebras
§ 6. Semi-simple Lie algebras
§ 7. Ado's theorem
Exercises
II. Free Lie Algebras
§ 1. Enveloping bigebra of a Lie algebra
§ 2. Free Lie algebras
§ 3. Enveloping algebra of the free Lie algebra
§ 4. Central filtrations
§ 5. Magnus algebras
§ 6. The Hausdorff series
§ 7. Convergence of the Hausdorff series (real or complex case)
§ 8. Convergence of the Hausdorff series (ultrametric case)
Appendix: Möbius function
Exercises
III. Lie Groups
§ 1. Lie groups
§ 2. Group of tangent vectors to a Lie group
§ 3. Passage from a Lie group to its Lie algebra
§ 4. Passage from Lie algebras to Lie groups
§ 5. Formal calculations in Lie groups
§ 6. Real and complex Lie groups
§ 7. Lie groups over an ultrametric field
§ 8. Lie groups over R and Qp
§ 9. Commutators, centralizers and normalizers in a Lie group
§ 10. The automorphism group of a Lie group
Appendix: Operations on linear representations
Exercises
Historical note
Bibliography
Index of notation
Index of terminology
Summary of certain properties of finite-dimensional Lie algebras over a field of characteristic 0