  In this paper we construct defects in coset $G/H$ theory. Canonical
quantization of the gauged WZW model $G/H$ with $N$ defects on a cylinder and a
strip is performed and the symplectomorphisms between the corresponding phase
spaces and those of double Chern-Simons theory on an annulus and a disc with
Wilson lines are established. Special attention to topological coset $G/G$ has
been paid. We prove that a $G/G$ theory on a cylinder with $N$ defects
coincides with Chern-Simons theory on a torus times the time-line $R$ with 2N
Wilson lines. We have shown also that a $G/G$ theory on a strip with $N$
defects coincides with Chern-Simons theory on a sphere times the time-line $R$
with $2N+4$ Wilson lines. This particular example of topological field theory
enables us to penetrate into a general picture of defects in semisimple 2D
topological field theory. We conjecture that defects in this case described by
a 2-category of matrices of vector spaces and that the action of defects on
boundary states is given by the discrete Fourier-Mukai transform.
