The aim of this work is to introduce some notions of Commitment as a descriptive ontology crucial for the understanding of groups’ and organizations' functioning, and of the relations between individual agents and collective activity. Some of the basic ingredients of such notions are identified and some steps are made towards their definition. In particular, it is claimed that a notion of Commitment is needed as a mediation between the individual and the collective one. Before constructing a notion of "Collective or Group Commitment" a notion of "Social Commitment" is to be defined. "Social commitment" is not an individual Commitment shared by many agents; it is the Commitment of one agent to another. The normative contents (entitlements / obligations) of this social relation are stressed and its connections with individual intentions and collective activity are alalized. On that basis, a notion of Organizational Commitment is proposed, that could account for the structure of stable Organizations. Commitment is a crucial notion both to analyse the structure of Organizations and to support cooperative work, but a deepex analysis is needed, connecting agent’s mental states with social relations and structure.