In this paper, we obtain the non-trivial Poisson brackets among the el
ements g in the group of dressing transformations, and the ones betwee
n g+/- and the chiral components xi and xiBAR of the Liouville field.
We also discuss the relation between the dressing transformation and t
he monodromy transformation of the Liouville field related to the unif
ormization theorem of Riemann surface.