The relevance of the article due to the fact that higher education in the third millennium is one of the most important factors for successful development of society, the necessary condition for sustainable competitive professional level personality matched due to the acquisition of knowledge and skills to provide employment, higher incomes, better working conditions. One of the forms in which higher education responds to the opportunities and challenges of globalization is internationalization. The documents which cover the international cooperation of universities and creating European Higher Education are analyzed. There are four strategies of internationalization of higher education: a coordinated approach; a strategy to attract qualified workforce; an income strategy; an empowerment strategy. The following goals are systematized: academic – the internationalization of the courses; organization of foreign training of the teachers, students, researchers, organization and participation of the teachers, students and researchers in the international conferences; international competitiveness and reputation of these schools; economic – University internationalization of economic activity: exports of educational and research services; attracting foreign students; foreign branch organization; implementation of distance learning programs; attraction of international grants for research activities. The multilevel nature of the process of internationalization of higher education is studied: international, national, university, individual. The predictions of cooperation between higher education institutions of the franchise, the program – «twins», mutual recognition of training programs are grounded. The author has determined internationalization as a factor in creating new opportunities and increasing the accessibility of higher education and its quality, innovative methods in higher education systems, strengthening international cooperation. The prospects for further research can be a problem of innovations in higher education, comparative analysis of the legal framework of European and Ukrainian higher education, complexity and discipline between the educational services, the intensification of international trade in educational services.