  We give a classification and complete algebraic description of groups
allowing only finitely many (left multiplication invariant) circular orders. In
particular, they are all solvable groups with a specific semi-direct product
decomposition. This allows us to also show that the space of circular orders of
any group is either finite or uncountable. As a special case and first step, we
show that the space of circular orderings of an infinite Abelian group has no
isolated points, hence is homeomorphic to a cantor set.
