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This chapter introduces and discusses the basic notions of decision-making in a multicriteria environment, namely, the set of feasible alternatives, the vector criterion and the preference relation of a decision-maker. Here we formulate the multicriteria choice problem. In addition, Chap. 1 defines a pair of fundamentally important notions, the set of nondominated alternatives and the Pareto set, which are vital for the statement and rigorous substantiation of the Edgeworth-Pareto principle.