Résumé
This thesis studies the moduli space of principal G2-bundles over a smooth connected projective curve, where G2 is the exceptional Lie group of smallest rank. The group G2 is introduced through three different ways, the first of them is the definition of G2 as the group of automorphisms of the complex algebra of the Cayley numbers. We study reductions and extensions that a principal G2-bundle can admit, as well as the link between a principal G2-bundle and its associated vector bundle in relation to the notion of (semi)-stability. The moduli space of semistable principal G2-bundles is analysed. We notably obtain a characterisation of its smooth locus, with an explicit decomposition of its singular locus into three connected components. We also give an analysis of the Verlinde space of G2 at level 1.