  We study the phases of a spin system on the Kagome lattice with
nearest-neighbor $XXZ$ interactions with anisotropy ratio $\Delta$ and
Dzyaloshinsky-Moriya interactions with strength $D$. In the classical limit
where the spin $S$ at each site is very large, we find a rich phase diagram of
the ground state as a function of $\Delta$ and $D$. There are five distinct
phases which correspond to different ground state spin configurations in the
classical limit. We use spin wave theory to find the bulk energy bands of the
magnons in some of these phases. We also study a strip of the system which has
infinite length and finite width; we find modes which are localized on one of
the edges of the strip with energies which lie in the gaps of the bulk modes.
In the ferromagnetic phase in which all the spins point along the $+ \hat z$ or
$- \hat z$ direction, the bulk bands are separated from each other by finite
energy gaps. This makes it possible to calculate the Berry curvature at all
momenta, and hence the Chern numbers for every band; the number of edge states
is related to the Chern numbers. Interestingly, we find that there are four
different regions in this phase where the Chern numbers are different. Hence
there are four distinct topological phases even though the ground state spin
configuration is identical in all these phases. We calculate the thermal Hall
conductivity of the magnons as a function of the temperature in the above
ferromagnetic phase; we find that this can distinguish between the various
topological phases. These results are valid for all values of $S$.In the other
phases, there are no gaps between the different bands; hence the edge states
are not topologically protected.
