  In this partly expository paper, we study the set A of groups of
orientation-preserving homeomorphisms of the circle S^1 which do not admit
non-abelian free subgroups. We use classical results about homeomorphisms of
the circle and elementary dynamical methods to derive various new and old
results about the groups in A. Of the known results, we include some results
from a family of results of Beklaryan and Malyutin, and we also give a new
proof of a theorem of Margulis. Our primary new results include a detailed
classification of the solvable subgroups of R. Thompson's group T .
