This edition provides a translation of two works by E. Cartana . The first work contains the most accessible statement of the essence of the method of the mobile rapper and the theory of finite continuous groups and in this respect can serve as a good introduction to the E. method. Cartana . The content of this work consists of lectures given by E. Cartan in Moscow at the Research Institute of Mathematics and Mechanics 16-20 June 1930 . These lectures are based on my notes; they were already published here in 1933. , but at present this edition has become a bibliographic rarity. The second, main work of this edition is the monograph . As the name itself shows, this work parallels the theory of finite continuous groups and gives an application of this theory to individual questions of differential geometry. All this is carried out by a single method - the method of a mobile rapper ..