The article is devoted to urgent problems of adaptation of a classical university to new conditions of the "knowledge society" and changes in information technologies. Contrary to dominating pessimistic forecast of the future for classical universities, the author acknowledges the increasing urgency of the problems of these educational institutions, appeals to the experience of leading universities in the world and shows new principles for functioning of universities in Russia, by examining the St. Petersburg State University. The author draws attention to tendencies of making use of virtual space to obtain up-to-date information and increase effectiveness of communication in the system of relations "university administration - teacher", "university administration - student", "teacher - student"; to get accessibility of students and teachers to the best electronic collections of foreign scientific journals, to the functioning scientific park with the resource centers which are oriented both to long-term fundamental research projects, and to the most needed ones in the short term period, etc. The article gives a careful consideration to a possibility of approaching classical universities to the model of "university 3.0".