Une introduction aux motifs: motifs purs, motifs mixtes, périodes

Motives were introduced 40 years ago by A. Grothendieck as a systematic theory of arithmetic properties of algebraic varieties as embodied in their groups of classes of cycles. This text provides an exposition of the geometric foundations of the theory (pure and mixed) and a panorama of major developments that have occurred in the last 15 years. The last part is devoted to a study of periods of motives, with emphasis on examples (polyzeta numbers, notably). It is suitable for graduate students and research mathematicians interested in number theory.