  We discuss and develop a systematic method to compute the Poisson center
(Casimir) of various Poisson algebras associated to loops on orientable
surfaces (possibly with boundary and punctures) introduced by Goldman and
Wolpert in 80's while studying Thurston's earthquakes deformations. Our
computation extends a result of Etingof to all finite type hyperbolic surfaces.
We use these methods to compute the center of various skein algebras introduced
by Turaev for the quantization of these Poisson algebras. As another
application of our results we compute the center of homotopy skein algebra
introduced by Hoste and Przytycki.
