  In [LMO] a 3-manifold invariant $\Omega(M)$ is constructed using a
modification of the Kontsevich integral and the Kirby calculus. The invariant
$\Omega$ takes values in a graded Hopf algebra of Feynman 3-valent graphs. Here
we show that for homology 3-spheres the invariant $\Omega$ is {\em universal}
for all finite type invariants, i.e. $\Omega_n$ is an invariant of order $3n$
which dominates all other invariants of the same order. This shows that the set
of finite type invariants of homology 3-spheres is equivalent to the Hopf
algebra of Feynman 3-valent graphs. Some corollaries are discussed. A theory of
groups of homology 3-spheres, similar to Gusarov's theory for knots, is
presented.
