As a natural extension of the Grand Unified Theories (GUTs), we have proposed the idea of Gauge-Yukawa Unification (GYU). The GYU is a functional relation among the gauge and Yukawa couplings provided by some principle. In our studies the GYU has been achieved by demanding the principles of reduction of couplings and finiteness. The first principle is based on the existence of renormalization group invariant (RGI) relations among couplings which preserve perturbative renormalizability in gauge theories. The second principle is based on the fact that it is possible to find RGI relations among couplings that keep finiteness in perturbation theory, even to all orders. We have examined the application of these principles in various models as well as the resulting predictions. in particular those connected with the masses of the top and bottom quarks. It is proposed to continue our research program in the above framework and to attempt to extend it. More specifically, we propose to : (i) Continue the studies in other supersymmetric GUTs, (ii) Refine the predictions by including a soft supersymmetry breaking sector and threshold effects, (iii) Extend the study in attempts to understand the light fermion masses and mixing angles, (iv) Reexamine the hierarchy problem of GUTs in the present framework, (v) Attempt to find links of the present scheme with superstrings as well as with other higher dimensional theories.