  We define a (co-)Poisson (co)algebra of curves on a bordered surface. A
bordered surface is a surface whose boundary have marked points. Curves on the
bordered surface are oriented loops and oriented arcs whose endpoints in the
set of marked points. We define a (co-)Poisson (co)bracket on the symmetric
algebra of a quotient of the vector space spanned by the regular homotopy
classes of curves on the bordered surface by generalizing the Goldman bracket
and the Turaev cobracket. Moreover, we define a Poisson algebra of unoriented
curves on a bordered surface and show that a quantization of the Poisson
algebra coincides with the skein algebra of the bordered surface defined by
Muller.
