  Previous work of the author has developed coordinates on bundles over the
classical Teichmueller spaces of punctured surfaces and on the space of cosets
of the Moebius group in the group of orientation-preserving homeomorphisms of
the circle, and this work is surveyed here. Joint work with Dragomir Saric is
also sketched which extends these results to the setting of the Teichmueller
space of the solenoid of a punctured surface, which is defined here in analogy
to Dennis Sullivan's original definition for the case of closed surfaces.
Because of relations with the classical modular group, the punctured solenoid
and its Teichmueller theory have connections with number theory.
