After arguing about the crucial importance of trust for Agents and MAS, we provide a definition of trust both as a mental state and as a social attitude and relation. We present the mental ingredients of trust: its specific beliefs and goals, with special attention to evaluations and expectations, We show the relation between trust and the mental background of delegation, We explain why trust is a bet, and implies some risks, and analyse the most basic forms of non-social trust (reliance on objects and tools) to arrive at the more complex forms of social trust, based on morality and reputation. Finally we present a principled quantification of trust, based on its cognitive ingredients, and use this "degree of trust" as the basis for a rational decision to delegate or not to another agent, The paper is intended to contribute both to the conceptual analysis and to the practical use of trust in social theory and MAS.
