The issue of diversity, in its broadest sense, is discussed here in its relation to social cohesion, cross-cultural relations, ingroup-outgroup relations and educational interventions. The main thesis of the paper is that real social cohesion in an ingroup rests on the acknowledgment of and the dialog with the diversities of the members of the ingroup itself. And that diversity relating to the outgroup and to the various members of the outgroup is understood and accepted, given that diversity among the members of the ingroup is also understood and accepted. This way, cross-cultural relations within an ingroup and between the ingroup and outgroups are fostered, which partly contradicts some traditional assumptions in social psychology research, according to which social cohesion in the ingroup is accompanied by hostility toward the outgroup. A study we conducted in Italian schools on youths' attitudes toward multiculturalism with the use of focus groups indicated that most participants have lost or have never experienced a feeling of general social cohesion. It also indicated that lack of social cohesion creates fear and that fear can provoke aggression. Some considerations are presented aiming to help teachers foster social cohesion and positive cross-cultural contact in their classes.