This article is devoted to the description of the competitive environment of the educational system of higher education. The directions and forms of competition of Russian universities are revealed in accordance with the constructive theory of competition. The article describes the classical theoretical directions of competition: product, industry, intersectoral, and inter-product competition. Product competition is the competition between manufacturers of interchangeable goods in the same distribution channels. It is a rivalry between competing product brands for distribution, otherwise known as trademark competition. Industry competition is the competition between producers of goods using homogeneous, interchangeable resources. In fact, this is competition for resources between producers of one sector, while there may be no product competition in distribution and sales. Inter-product competition is the competition between substitutes from different industries, that is, between representatives of different industries - manufacturers of products that satisfy the same need. Cross-industry competition is the competition of corporate brands in marketing, the general competition of all brands to attract the attention of a certain segment of consumers. The article shows that all four directions of competition appears in their forms in the activities of Russian universities. The specific forms of competition between Russian universities are revealed. Competition among universities appears in different forms: for social authority and influence; for statuses, titles, and prestige; for exclusive intellectual property, massive data sets, and computing power; for the talents of students; for the talents of teachers; for budget funding; for grant, competitive financing; for donations and endowment funds. Special attention is paid to the forms of competition within partnerships and cooperation between universities. In this form, the bargaining power is used in the distribution of value between the participants in the partnership.