  We introduce the notion of Galois holomorphic foliation on the complex
projective space as that of foliations whose Gauss map is a Galois covering
when restricted to an appropriate Zariski open subset. First, we establish
general criteria assuring that a rational map between projective manifolds of
the same dimension defines a Galois covering. Then, these criteria are used to
give a geometric characterization of Galois foliations in terms of their
inflection divisor and their singularities. We also characterize Galois
foliations on $\mathbb P^2$ admitting continuous symmetries, obtaining a
complete classification of Galois homogeneous foliations.
