The book contains a comprehensive account of the structure and classification of Lie groups and finite-dimensional Lie algebras (including semisimple, solvable, and of general type). In particular, a modern approach to the description of automorphisms and gradings of semisimple Lie algebras is given. A special chapter is devoted to models of the exceptional Lie algebras. The book contains many tables and will serve as a reference. At the same time many results are accompanied by short proofs. Onishchik and Vinberg are internationally known specialists in their field and well-known for their monograph “Lie Groups and Algebraic Groups” (Springer-Verlag 1990). This Encyclopaedia volume will be immensely useful to graduate students in differential geometry, algebra and theoretical physics.