  The Becchi-Rouet-Stora and Tyutin (BRST) transformation plays a crucial role
in the quantization of gauge theories. The BRST transformation is also very
important tool in characterizing the various renormalizable field theoretic
models. The generalization of the usual BRST transformation, by making the
infinitesimal global parameter finite and field dependent, is commonly known as
the finite field dependent BRST (FFBRST) transformation. In this thesis, we
have extended the FFBRST transformation in an auxiliary field formulation and
have developed both on-shell and off-shell FF-anti-BRST transformations. The
different aspects of such transformation are studied in Batalin-Vilkovisky (BV)
formulation. FFBRST transformation has further been used to study the
celebrated Gribov problem and to analyze the constrained dynamics in gauge
theories. A new finite field dependent symmetry (combination of FFBRST and
FF-anti-BRST) transformation has been invented. The FFBRST transformation is
shown useful in connection of first-class constrained theory to that of
second-class also. Further, we have applied the Batalin-Fradkin-Vilkovisky
(BFV) technique to quantize a field theoretic model in the Hamiltonian
framework. The Hodge de Rham theorem for differential geometry has also been
studied in such context.
