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These are lectures notes on rationally connected varieties, written for the"Etats de la Recherche" of the French Mathematical Society held in Strasbourg(May 2008). We focus on geometric aspects. These notes have been written inorder that a wide audience can easily read them, except maybe the last section,a bit more technical, where we give the proof of Shokurov rationalconnectedness conjecture following Hacon and McKernan.    Ce sont les notes d'un mini-cours sur les vari\'et\'es rationnellementconnexes, \'ecrit pour les Etats de la Recherche de la Soci\'et\'eMath\'ematique de France (Strasbourg, 2008). On met l'accent sur les aspectsg\'eom\'etriques. Ce cours est r\'edig\'e dans l'espoir de s'adresser \`a unpublic large, \`a l'exception peut-\^etre du \S 7, o\`u nous donnons lesgrandes lignes de la preuve de la conjecture de connexit\'e rationnelle deShokurov par Hacon et McKernan, plus technique et o\`u les pr\'erequis sont unpeu plus importants.

Vari\'et\'es rationnellement connexes sur un corps alg\'ebriquement clos