  In this paper we present a generalization of Poincar\'e's Rotation Theory of
homeomorphisms of the circle to the case of one-dimensional compact abelian
groups which are solenoidal groups, {\it i.e.}, groups which fiber over the
circle with fiber a Cantor abelian group. We define rotation elements,
\emph{\`a la} Poincar\'e and discuss the dynamical properties of translations
on these solenoidal groups. We also study the semiconjugation problem when the
rotation element generates a dense subgroup of the solenoidal group. Finally,
we comment on the relation between Rotation Theory and entropy for these
homeomorphisms, since unlike the case of the circle, for the solenoids
considered here there are homeomorphisms (not homotopic to the identity) with
positive entropy.
