Th\'eorie-M sur des Vari\'et\'es d'holonomie G2

We study the reduction of 11- dimensional M-theory to (3 +1) dimensions with four conserved supersymmetric charges by following the work of B. Acharya and E. Witten [arXiv:hep-th/0109152]. We first review the various 10D superstrings models, their compactifications to lower dimensions, string/string dualities and links with M-theory. Then, we study compactifications of M-theory first on K3 with ADE singularities; and second on both regular and singular real 7-dimensional G2 manifolds. Others features, such as non abelian 4D quiver gauge models, are also discussed.