This almanac initiates a series of edited volumes dedicated to various aspects of the application of mathematical methods to the study of history and society. It comprises articles that apply mathematical methods to the study of various epochs and scales: from deep historical reconstruction to the pressing problems of the modern world. On the other hand, all the articles of this almanac are dedicated to the analysis, periodization, or modeling of global development. It is shown that the mathematical modeling of historical macroprocesses suggests a fresh approach to the periodization issue. The authors study these problems from different perspectives (technological, economic, demographic, sociostructural, cultural-psychological, linguistic). New quantitative insights on the dynamics of contemporary processes are presented. These insights allow the authors to make a number of important forecasts on this basis.