  Motivated by the classical studies on transformations of conjugate nets, we
develop the general geometric theory of transformations of their discrete
analogues: the multidimensional quadrilateral lattices, i.e. lattices x: Z^N ->
R^M, whose elementary quadrilaterals are planar. Our investigation is based on
the discrete analogue of the theory of the rectilinear congruences, which we
also present in detail. We study, in particular, the discrete analogues of the
Laplace, Combescure, Levy, radial and fundamental transformations and their
interrelations. The composition of these transformations and their
permutability is also investigated from a geometric point of view. The deep
connections between "transformations" and "discretizations" is also
investigated for quadrilateral lattices. We finally interpret these results
within the D-bar formalism.
