  In this paper, we introduce and study the notion of linkage of modules by
reflexive homomorphisms. This notion unifies and generalizes several known
concepts of linkage of modules and enables us to study the theory of linkage of
modules over Cohen-Macaulay rings rather than the more restrictive Gorenstein
rings. It is shown that several known results for Gorenstein linkage are still
true in the more general case of module linkage over Cohen-Macaulay rings. We
also introduce the notion of colinkage of modules and establish an adjoint
equivalence between the linked and colinked modules.
