The article considers the main competences (informational, communicational, competences of thinking, self-organizing and self-orienting) at different stages of higher education, i.e. among people with incomplete higher education, with the Bachelor or Master’s degrees, with the Specialist diploma or people with post-graduate degrees. The competences listed determine educational programs according to the scientific discipline. The study discovered three main strategic directions for an intensively active personally oriented educational training: subject-oriented teaching; developing students’ subject attitude to studying and gaining professional knowledge; students’ individual work controlled by teachers, as a new form of self-studying at the modern university.