Abstract
This thesis is about modular decomposition of graphs. The first part of the manuscript is devoted to theory. First it is question of set decompositions that have the same properties than modular decomposition : the partitive families, and three variations. Then are presented some graph decompositions that extend modular decomposition, using the notion of 2-modules (homogeneous pairs). This is the case for the split decomposition of Cunningham, and also for the new 2-joins and sesquimodules decompositions. A analog of modules for bipartites graphs,,the bimodule, leads to a decomposition theory very near the modular decomposition of directed graphs. The second part is practical and presents modular decompositions algorithms for undirected graphs, tournaments, directed graphs, interval graphs and permutation graphs. All these algorithms run in linear-time from the input : O(n + m) for the three first classes, O(n) for the two last classes, in the graph is coded with an interval or permutation model.