In this paper are studied the evolution, content and problems of quality management, as science and education subject. There are also analysed the aspects of quality managers’ formation in the universities. This article was written using scientific, normative and legal literature, systemising the good practices of Western countries’ universities’, international organisations’ of quality and business enterprises and the results of author’s performed systematic researches of quality problems. The author suggests such alternate descriptions of quality in general, quality of life, social responsibility and total quality management (TQM). Quality of life is dependent on material status (quality of products, accommodation etc.), environmental surrounds and sustainable development of economics, community health, levels and quality of education, the moral and psychological climate in society, organisation and family. Quality management master’s programme of Vilnius University in 2004 got international accreditation and good evaluation of experts. Author formulated suggestions for the formation of quality managers in the universities of Lithuania and proposed TQM and knowledge management integrated model.