We considered the problems, prospects, and tools for intercultural dialogue in the universities of Russia from the position of their generalization and identification of the successful experience for its extrapolation and implementation in other higher education establishments. The methodology of this research is comprised of complex tools, which lie in the dimension of a range of sciences of the sphere of sociology, political sciences, cultural sciences, pedagogics, ethnopsychology, etc. Focus was made on the concept of polyphony and mutual self-cognition, and the potential of intercultural dialogue from the position of its influence on the development and effectiveness of socio-cultural systems. The methodology of this research consists of empirical and theoretical methods of analysis of scientific and expert works and information from open sources. We studied theoretical and institutional aspects of international migration, including in the sphere of higher education. We determined the components intercultural dialogue from the position of achieving mutual understanding and interest in intercultural exchange. We identified the specific features and problems of intercultural communications in Russian universities and generalized and characterized the experience of successful measures in adapting students to the multicultural educational environment and creating of conditions for effective intercultural dialogue in multinational classical universities of Russia. The value and originality of this work lie in the generalization of the practical experience of the organization of space for intercultural dialogue in multinational classical universities of Russia from the position of its extrapolation and dissemination in other educational establishments. [For the complete volume, "University 4.0 and Educational Technology for Sustainable Development: Best Practices and Perspectives in Russia and Central Asia. Education in the Asia-Pacific Region: Issues, Concerns and Prospects. Volume 75," see ED675741.]