Identification and critical study of social-political aspects of contemporary society within conditions of globalization must start from the characteristics (essence) of globalization as a process of human kind consolidation. Globalization represents a process of economic, political and cultural connecting of all separate mankind societies (specific societies) into the one whole, into a 'World' - 'Global' society (mega-society) on the Planet with many contradictions. It is a meaningful way for money to bring profit in a peaceful manner. It leads not only to expanding of economic power through transnational and multinational economic corporations, but also to imposing way of life, social organization and categorized value system of countries - protagonists of globalization to others, as indicators of their creative capabilities and specific forms of their appearance, specialty and durability. These and other changes, as well as multiple and versatile consequences that accompany them, indicate the necessity of constructing a new social approach in their scientific cognition, with full respect of not only social but also natural laws on cognition and estimation of accomplishing social life. The social and especially sociological sciences should investigate and excogitate the next areas of global reality of contemporary society in this context. Macrostructures in the architecture of its construction: world community, socio-economic system that appears with globalization process and international community that appears by agreement between the states, their dynamic relationship and influence on flows and future of mankind civilization and social position of human. Diversity of the forms of cooperation, conflicts and collisions in the 'world' society and possibility of war conflicts regarding safety of not only specific people, regions and states, but also regarding the survival of human civilization, since it is obvious that such a conflict would have planetary and cosmic consequences. Dignity of man and his work, regarding the global character of economic life, whose bearers are multinational corporations, and global character of job market, regarding preservation of dignity of work as presumption of preservation of dignity of man. However, the question is if the contemporary level of science development allows this, first of all social sciences and especially sociology (which is generally determined as the most general science on society and its totality). In fact, the question is if the theoretical-cognitive apparatus of sociology allows studying of the complex structure and category of contemporary society and their dynamics of changes that are not accompanied by development of suitable idea-terminological apparatus. As Sorokin points out, many theories have appeared in sociology since Auguste Comte that had their boom, and then they were contested and finally disappeared. Considering the problems of sociological theories, it should be born in mind that a 'universal' sociological theory cannot exist because few theoretical-methodological attitudes are not enough to interpret accelerated complexity of social development dynamics, and the society is changing very fast. However, it is possible to specify the theory parameters in the context for valid interpretation of development tendencies of self-development of society. Tendency of postmodernism to make the society in its construction and dynamics by its subject of study, especially by establishing postmodern sociological terminology, indicates tendency that postmodernism paradigm questions the referred determinacy of sociology itself, which has been developed and survived as science on classical terminology. A danger exists that paradigm arisen from tendency to modernize cognitional apparatus of sociology (the terms) questions existence of the science itself within which it has originated, i.e. sociology. Therefore, postmodern sociological paradigm should be also studied critically, together with tendencies to build a new developing terminal categorical system of sociology, adequate to cognition on achieved changes in society.