  A clover is a framed trivalent graph with some additional structure, embedded
in a 3-manifold. We define surgery on clovers, generalizing surgery on Y-graphs
used earlier by the second author to define a new theory of finite-type
invariants of 3--manifolds. We give a systematic exposition of a topological
calculus of clovers and use it to deduce some important results about the
corresponding theory of finite type invariants. In particular, we give a
description of the weight systems in terms of uni-trivalent graphs modulo the
AS and IHX relations, reminiscent of the similar results for links. We then
compare several definitions of finite type invariants of homology spheres
(based on surgery on Y--graphs, blinks, algebraically split links, and boundary
links) and prove in a self-contained way their equivalence.
