  Three dimensional topological field theories associated with the three
dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are
presented. These three dimensional monopole equations are obtained by a
dimensional reduction of the four dimensional ones. The starting actions to be
considered are Gaussian types with random auxiliary fields. As the local gauge
symmetries with topological shifts are found to be first stage reducible,
Batalin-Vilkovisky algorithm is suitable for quantization. Then BRST
transformation rules are automatically obtained. Non-trivial observables
associated with Chern classes are obtained from geometric sector and are found
to correspond to those of the topological field theory of Bogomol'nyi
monopoles.
