Italian Universities, under some social, cultural and economic pressures, have been called to change the institutional action adding to the two traditional missions, on the one hand the Didactics for a qualified training and on the other the Research, a new objective (called "Third Mission") aimed at continuous interaction with the social environment, school institutions and the business world to create the basis for a common project of development. The aim of the paper is to analyze the change of Italian university system through the evolution of the two traditional functions and illustrate a new path within which the University should promote the growth of the person through the acquisition of competence and awareness, and also the constructive dialogue between historically distinct systems: education, research and innovation.