Th\'eorie de jauge et groupo\"i des (Gauge theory and groupoids)

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such as gauge theory, lattice gauge fields, equivariant bundles, etc. In the course of the proofs, some new facts about Milnor's classifying spaces and gauge groups are established.