The first University was founded in Bologna in the early XIIth century, and the second one in Paris by the end of the same century. By 1300, there were already 16 universities existing in Italy, France, England and Spain. By the XIVth century, 30 more were added including in Austria, Poland and Bohemia. By 1500, there were as many as 60 universities. The University granted a “Licentia Docenti” as a teachers’ union, which was an authorization to teach that intended: the understanding of the classics and argumentative capacity. At some universities such as the one in Salamanca, whose model would be implemented in Latin America, the vision of the medieval world prevailed associated with the predominance of the Catholic Church’s conceptions which were widely promoted. Meanwhile, other universities such as in Oxford in England, openly stimulated modernizing concepts developed by intellectuals such as Francis Bacon, where the inductive method was acknowledged as the way to scientific knowledge. Those institutions opened spaces to new content for teachings, including skills for agriculture, industry and commerce. The universities redefined their mission and purpose, or returned to earlier conceptions, resulting in a history full of irony and ambiguity, overrun with and the resetting of ideals lost and recovered. To understand that history requires that we recount how the universities had faced the classes or specific categories of educational types and levels: Liberal Arts, Professions, Science, Technology, Research and Vocation.