The article analyzes the concept of the quality of higher education and approaches to its provision. The essence of the understanding of high-quality professional training by domestic and foreign scientific and pedagogical workers is considered. Attention is focused on the multifaceted phenomenon of the quality of higher education and the variety of ways and methods of its provision. The results of a theoretical analysis of the features of the educational process at the leading universities in the QS World University Rankings: Massachusetts Institute of Technology, Oxford, Stanford, Harvard and Cambridge are highlighted. A conclusion was made about the importance of introducing or intensifying the use in domestic institutions of higher education of the following methods of improving the quality of education of applicants: research projects, lectures of a dialogic nature with the analysis of actual cases, writing creative essays during independent work based on the study of given scientific sources, seminars-discussions with encouragement students to ask a large number of questions and find answers to them, preparing students for the lecture by studying the scientific literature on its topic, individual interviews on the subject of the classes, invitations to separate lectures by well-known narrow-profile specialists in the relevant field.