Contemporary universities are facing challenges that cause doubts about its future: "Abelard's University" still has a future at the time of the Shangai Ranking? In view of the fact that the teacher formation was the main objective of the universities of the 20th century, what will be its destination in universities that have to focus research? The articles starts with a sketch of the ideal type of the university: what in it must remain so that one still can speak of "university"? It considers eight characteristics, sending to the professors, its activities, its relations with powers, environment and others institutions of education. To follow, it is proven that the formation of the teacher of primary education was outside of the missions of the universities, until recently, but that of the teacher of secondary education was the central project of the universities in the modern times. Why this difference? Finally, the main contemporaries evolutions of superior education are analyzed: internationalization, mercantilization and differentiation. Some hypotheses are advanced on what will be the teacher formation in those universities of the 21st century.
university; teacher formation; contemporary society