The authors of the article address the origins of appearing and developing of the main idea of the article in order to correctly identify the notion and the purpose of the idea of the civil society. The authors research various points of view on the issue of the connection of the State and the civil society. The authors of the article point out the peculiarities of the process of forming of the civil society in Russia. The authors give the definition of the notion of “civil society” and point out its features. Despite the fact that the legal definition for the “institutes of the civil society” does not exist, the authors underline that the term is used broadly in the existing federal and regional legislation. Basing their research on the opinion of scientists about the legal nature and structure of the civil society, the authors give the definition for the “institute of the civil society”. They present the classification of the institute of the civil society using different criteria. According to this classification, the institutes are divided because of their status differences, functional orientation, level of participation in law enforcement activities, prevention of offences etc. The authors point out that the institutional approach to classification of the institutes of the civil society is widely spread because it allows distinguishing and describing some separate subjects of the civil society that exercise certain interests. The authors conclude with the explanation of why non-profit organizations are viewed as the institutes of the civil society. They point out that any state corporation, self-regulating organization that is represented as a non-profit organization cannot be viewed as an institute of the civil society because they perform public functions of the State. That is why only some part of non-profit organizations can be viewed as institutes of the civil society; they should have such features as voluntary nature, self-regulation, self-organizing, self-activity and self-responsibility.