  In this thesis, we develop techniques for the analysis of SO(2N) invariant
couplings which allows a full exhibition of the SU(N) invariant content of the
spinor and tensor representations. The techniques utilize a so called Basic
Theorem which we first derive. Using this method an evaluation of the trilinear
couplings of the 16 plet of matter and of the 16 and $\bar{16}$ plets Higgs is
given. In particular, we give a full determination of couplings in their SU(5)
decomposed form, involving $16 16$ and the 10, 120 and $\bar{126}$ tensor
fields together with $\bar{16} 16$ ($16 \bar{16}$) and the 1, 45 and 210 tensor
fields. We also compute the vector couplings of $16 16$ ($\bar{16} \bar{16}$)
and the 1, 45, 210 gauge fields. Computation of dimension-5 operators formed
from 16 and $\bar {16}$ arising from the mediation of 1, 10, 45 and 210 plet of
heavy Higgs, are also analyzed. Complete supersymmetric vector couplings
belonging to the singlet and the adjoint representation of the SO(10) gauge
group are computed in the Wess-Zumino gauge. An $SU(5)\times U(1)$
decomposition of the vector couplings ${16}-16-210$ is completely carried out
using the Wess-Zumino gauge and its transition to a non linear sigma type model
is shown. The utility of these results in the analysis of quark-lepton textures
and of proton decay is briefly discussed. Possible future applications of the
techniques given here such as in the development of string landscape SO(10)
type models is briefly pointed out.
