  It is shown that superfluids in two and three dimensions which have time
reversal invariant ground states have phases which are distinguished by a
topological invariant. Further, it is shown that the B-phase of $^3$ He is a
superfluid in the non-trivial topological class. Superfluids in the non-trivial
topological class are shown to have gapless edge states and support various
kinds of vortices with zero energy modes localized in their cores. Some of
these vortices have non-abelian statistics.
