  There are many topological faces of the superfluid phases of $^3$He. These
superfluids contain various topological defects and textures. The momentum
space topology of these superfluids is also nontrivial, as well as the topology
in the combined (${\bf p},{\bf r})$ phase space, giving rise to topologically
protected Dirac, Weyl and Majorana fermions living in bulk, on the surface and
within the topological objects. The nontrivial topology lead to different types
of anomalies, which extended in many different directions the
Landau-Khalatninkov theory of superfluidity.
