  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.
