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BRST symmetry provides a basis for the modern quantization of gauge theory. It can be generalized depending on whether the transformations are finite field-dependent, local or non-local. A BRST method also provides an elegant and powerful tool for the construction and analysis of constrained systems in 1-form and 2-form gauge theory which requires the Hamiltonian formalism. This book is based on the generalization of BRST transformations and its application to various gauge theories in both Lagrangian and Hamiltonian formalism.