The author presents his approach, which allows him to view society as a whole: its components (personality, culture, socium), types of their correlations, functions, processes, stages of evolution. The person as a real actor is not lost in the mass of contemporary socium, but has a possibility to rise to the same level as it. This is the essence of the anthroposocietal approach. What is it based on? The author offers an understanding of society as a nonequilibrium anthroposocietal system, which is under the threat of the catastrophic risks, but can change in response to them and provide stabilization and order from crisis and chaos. This understanding based on closely connected principles, including the principle of incomplete reciprocal accordance between the personality and the socium, is the central. The actual problems of the individual’s massification in various societies and the individualisation of the societies of the other modernity are examined. The European Union is characterized as the anthroposocietal system of a new type – among the states and among the citizens of these states. The accent is made on the necessity to enhance the modern qualities of the Russian society.