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A classically rational subject is a maximiser: he chooses the best alternative(s) according to some utility function, a paradigm going back to the eighteenth century. One of the ways to overcome its well-known deficiences is to extend it to take into account insenitivity threshold as well as the context of choice. This book gives a systematic overview on the extended utility maximisation theory covering the classic theory, the theory of utility maximisation within a context-free or context-dependent threshold, and the related preference and choice models. The presented models will be helpful to specialists in economics, decision making theory, social choice theory, behavioral and cognitive sciences, and related fields.