In this work the problem of the Uyadic Green's Functions ( DGF ) is investigated so, that a more rigorous foundation of their theory and a clarification of the origin and meaninq of their symmetrical properties is obtained. The adjoint problem is formulated, the UGFs for all possible cases of boundary conditions for the Vector Helmholtz equation are defined and their symmetrical properties, as well as the assumptions under which these ones hold, proved. The analysis begins with the examination of the basic problem of the DGF for a finite homoqeneous space, which results to a more general statement of the Love equivalence theorem and the investigation of the possibilities on the choice among more DGFs for the solution of a problems: it passes to the problem of two spaces in contact (two layered medium), where the coupling relation between the two DGFs is determined and oroved to be arbitrary in the general case; and, finally, it is generalised for the case of a medium with arbitrary number of layers.