  The theory of $G$-structures provides us with a unified framework for a large
class of geometric structures, including symplectic, complex and Riemannian
structures, as well as foliations and many others. Surprisingly, contact
geometry - the "odd-dimensional counterpart" of symplectic geometry - does not
fit naturally into this picture. In this paper, we introduce the notion of a
homogeneous $G$-structure, which encompasses contact structures, as well as
some other interesting examples that appear in the literature.
