  In the present paper we study geometric structures associated with webs of
hypersurfaces. We prove that with any geodesic (n+2)-web on an n-dimensional
manifold there is naturally associated a unique projective structure and,
provided that one of web foliations is pointed, there is also associated a
unique affine structure. The projective structure can be chosen by the claim
that the leaves of all web foliations are totally geodesic, and the affine
structure by an additional claim that one of web functions is affine.
  These structures allow us to determine differential invariants of geodesic
webs and give geometrically clear answers to some classical problems of the web
theory such as the web linearization and the Gronwall theorem.
