Mathematical Feature of Gauge Theory

In this paper, we deal with root of gauge theory and constrained system. Considering unlike second class constrained leads to non-gauge theory, all theories with first class constraints are gauge theory. We consider two mathematical and systematic methods, BFT approach and Gauge Unfixing formalism which do conversion of non-gauge theory into gauge one. Despite of noble similarities of two methods, they have primordial different which mentioned. In the end, we figure out these methods for two impressive models which are interesting in their own.