Abstract
The central theme of this thesis is the study of the properties of the classes of graphs defined by forbidden substructures and their applications. The first direction that we follow concerns well-quasi-orders. Using decomposition theorems on graph classes forbidding one substructure, we identify those that are well-quasi-ordered. The orders and substructures that we consider are those related to the notions of contraction and induced minor. Then, still considering classes of graphs defined by forbidden substructures, we obtain bounds on invariants such as degree, treewidth, tree-cut width, and a new invariant generalizing the girth. The third direction is the study of the links between the combinatorial invariants related to problems of packing and covering of graphs. In this direction, we establish new connections between these invariants for some classes of graphs. We also present algorithmic applications of the results.