Its first part, which is written by Onishchik and Vinberg, is an introduction to the theory of Lie groups and Lie algebras. The second more advanced part by Gorbatsevich and Onishchik deals with Lie transformation groups and covers the work of the last decades including the most recent research results. The book is written for graduate students and researchers in mathematics and theoretical physics.

Inhalt
I.Foundations of Lie Theory.- 1. Basic Notions.- 2. The Relation Between Lie Groups and Lie Algebras.- 3. The Universal Enveloping Algebra.- 4. Generalizations of Lie Groups.- II. Lie Transformation Groups.- 1. Lie Group Actions on Manifolds.- 2. Transitive Actions.- 3. Actions of Compact Lie Groups.- 4. Homogeneous Spaces of Nilpotent and Solvable Groups.- 5. Compact Homogeneous Spaces.- 6. Actions of Lie Groups on Low-dimensional Manifolds.