This book proposes a formalisation of emotions in a BDI logic (logic of belief, desire and intention). Such a formalisation aims at helping the design of emotional agents. The first part is dedicated to the state of the art, from the point of view of both psychology (history of theories of emotions) and computer science (emotional agents and their applications). The second part is dedicated to the logical formalisation of emotions; it introduces the logical framework, exposes and argues the formal definitions of twenty emotions, and proves some of their properties. Finally the last part is dedicated to practical applications and continuation prospects of this work. Such a work offers interesting contributions: it provides the agent community with a formal model of a great number of emotions; it shows the interest of BDI logics; and it opens research prospects about the dynamics of emotions and their influence on the behaviour of agents, a field not much explored yet.