The article is devoted to the problems of integration processes and the implementation of integration in the space of the Russian Federation by organizing joint activities in the educational sphere. The means of implementing the integration function are University profile educational sessions (University sessions). To determine and describe the basic principles of the indicated function, the authors analyze studies devoted to the retrospective of the analyzed process, modern integration experience, the specifics of the implementation of the integration function in a specific form of organization. The basic principles formulated by the authors are distributed according to the components of the pedagogical process: targeted, meaningful, procedural assessment. The target component for university sessions defines the principles concerning the unification of the university staff and university sessions participants for joint activities, the focus of university sessions on education, the multicultural educational space of university sessions, qualitative and quantitative planning of sessions results. The content component defines principles regarding the inclusion of variable and invariant parts of the program, dynamic and adaptive content. The procedural component defines the principles of joint activities in group and individual formats, ensuring equal opportunities for all participants, the choice of methods, forms and means of joint activities that reflect the best experience of domestic education. The evaluation component involves the systemic use of diagnostic tools, the implementation of constant monitoring. Based on the analysis, the concept of the integration function of the University session at the university is also formulated.