An integrated system of quality management at a university includes the modules of strategic management and of management of process quality based on the ISO 9001:2008 standard. That includes the education process, which is decomposed into components having to deal with the planning of graduates’ competences, the development and implementation of the basic curriculum of the university, and the management of the education process on the basis of the European ESG standards, and their external assessment according to international accreditation criteria. As an example, the authors use the integrated system of quality management at the Tomsk polytechnic university.