The first volume of Claude Chevalle's monograph on Lie group theory was published in the United States in 1946. ; in 1951. A second volume was published in France, and in 1955. The Third . The translation of the first volume was published by the Foreign Literature Publishing House in 1948. ; the translation of the third volume will be published shortly after the translation of the second volume. The present, second volume is devoted to the presentation of the theory of algebraic groups (groups of matrices given by algebraic relations between coefficients), a theory that has developed in recent years to a large extent in the works of the author himself. This is the first systematic exposition of the theory of algebraic groups in the world. The third volume is devoted to the theory of Lie algebras . The book is designed for mathematicians - undergraduates, graduate students and researchers .