This is the text (in French) of the 2002 Universit\'e Paris 13 doctoral thesis of Fr\'ed\'eric Jean: "Foncteurs d\'eriv\'es de l'alg\`ebre sym\'etrique: Application au calcul de certains groupes d'homologie fonctorielle des espaces $K(B,n)$" (together with a May 2009 list of errata). Abstract: A study of the derived functors of the symmetric algebra and related functors. With applications to the functorial computation of certain homology groups of Eilenberg-Mac Lane spaces.