In the monograph, for the first time, the archaeological era was investigated as an integral phenomenon, as a large open system. A mathematical model of the chronology and periodization of the era, built on the basis of numbers and the Fibonacci series, is proposed. The stages of evolution are described, a mathematical model of the general development of the archaeological era is presented, the magnitude of the acceleration of these processes is found. The book may be of interest to archaeologists, ethnologists, historians of primitive society, historians of ancient industries, sociologists, as well as philosophers who would like to learn more about the initial stages of the development of processes occurring in our time.