In this article, we present the results of the development of the “Political Atlas of the Modern World” (“Atlas 1.0”) project. “Atlas-1.0” was implemented more than ten years ago by scholars of the MGIMO University with the support of the Institute of Public Projects and the “Expert” magazine. Development of five complex indices – of stateness, external and internal threats, the potential of international influence, the quality of life and the institutional foundations of democracy – was one of the major results of the “Atlas-1.0” project. The method of discriminant analysis was used to calculate the ratings of 191 UN member states (as well as Taiwan) as of 2005. The results obtained, reflecting various aspects of the existence of modern states, were compressed into four principal components. The four of them in the complex were interpreted as an analytical model of the modern world structure. In the project implemented ten years later at the Higher School of Economics with the support of a grant from the Russian Science Foundation (“Atlas 2.0”), the results obtained in the earlier atlas were tested for durability, corrections were made for the emergence of new UN member states, the components of the indices were refined, new statistical databases were used and advanced methods of ultivariate statistical analysis were employed. The performed operations fit into the tradition of “revisited” which is part of the modern social sciences. A number of meaningful conclusions about the dynamics of the world structure have been made. The results obtained (configurations of the principal components) indicate the significant stability of the basic parameters of the world structure. At the same time, important elements of dynamics have also been revealed.