The paper presents historical concepts and paradigms of the institution of university as well as its present and future models.The origin, structure and function of the medieval university are discussed; then, four basic concepts of university formed in the 19th century are given. What follows is an analysis of the changes and evolution of universities in the 20th century. It is indicated that the essence of today's university is composed of the following activities: didactics, research and professional training. The priority is given to practising basic disciplines at universities and the significance of the humanities for general education of students, including philosophy, theology and ethics is stressed. The author is warning us against single-discipline education in a situation when all contemporary problems can only be solved on the interdisciplinary basis via cooperation of experts in different fields. The gap between visions of the world shaped by natural sciences and the humanities should be gradually bridged. To this end, a paradigm of the future university is put forward. The paradigm should provide for cultivation of the values derived from the Classical University rooted in the Greco-Roman and Christian tradition, mathematical exactness of scientific research and quality professional training of the Positivist University, as well as the ecological and holistic vision and education of the youth, in a spirit of tolerance of the Post-modern University. The paradigm of the university of the future should encompass three significant elements, i.e. the mission of a contemporary academic school, the conditions in which it is functioning and the rules it should follow. The paper indicates that, though destined to an ongoing change, the mission of universities for centuries has featured the same components, namely intellectual and ethical education of the youth and scientific research. The contemporary university should act as 'the eyes of the world' that perceive its main problems and provide guidance in solving them. The contemporary university must duly take into account the external conditions, namely globalisation, multiculturalism, ecological threats, rapid communications and technological progress, a growth of negative social phenomena such crime, moral degradation and terrorism; a growing influence of the media on life of societies, anti-intellectualism, relativism and radical individualism triggered by the Post-modem era. The rules that a contemporary academic school should act in accordance with are given as follows: a quest for the highest standards in didactics, research and other activities; full freedom of scientific research; a focus on discovering the truth and sharing it with others; ethical responsibility of scholars and university professors; the spirit of duty in education; forming amicable and stable academic communities; partnership in cooperation with other scholars and universities; aiming at the integration of Christian knowledge and faith. The paper ends with a citation from Pope John Paul's II. address (1997) to the chancellors of all Polish academic schools,
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