Geometrical properties of point correspondences of three conformal spaces

We study point correspondences of three conformal spaces on the base of G. F. Laptev invariant methods. We define the main equations and geometrical objects of correspondences. We construct invariant normalizations of spaces, describe the main tensors of correspondences, establish the connection of the correspondences under consideration with the theory of multidimensional $3$-webs, and obtain the torsion and curvature tensors for correspondences. For certain particular cases we prove existence theorems.