This book is one of the best manuals for studying the theory of Lie algebras. It sets out in detail the foundations of the theory: solvable algebras, nilpotent algebras, Lie and Engel theorems, the theory of semisimple Lie algebras, root systems. Classical results on the construction of a semisimple Lie algebra by its root system are discussed. Separate chapters are devoted to representation theory and the theory of Chevalley groups and algebras.