  We describe the symplectic reduction construction for the physical phase
space in gauge theory and apply it for the BF theory. Symplectic reduction
theorem allows us to rewrite the same phase space as a quotient by the gauge
group action, what matches with the covariant phase space formalism. We extend
the symplectic reduction method to describe the phase space of the initial data
on a slice with boundary. We show that the invariant phase space has
description in terms of generalized de Rham cohomology, what makes the
topological properties of BF theory manifest. The symplectic reduction can be
done in multiple steps using different decompositions of the gauge group with
interesting finite-dimensional intermediate symplectic spaces.
