  By implementing four-wave mixing (FWM) micro-spectroscopy we measure
coherence and population dynamics of the exciton transitions in monolayers of
MoSe$_2$. We reveal their dephasing times T$_2$ and radiative lifetime T$_1$ in
a sub-picosecond (ps) range, approaching T$_2$=2T$_1$, and thus indicating
radiatively limited dephasing at a temperature of 6$\,$K. We elucidate the
dephasing mechanisms by varying the temperature and by probing various
locations on the flake exhibiting a different local disorder. At a nanosecond
range, we observe the residual FWM produced by the incoherent excitons, which
initially disperse towards the dark states, but then relax back to the
optically active states within the light cone. By introducing
polarization-resolved excitation, we infer inter-valley exciton dynamics,
showing an initial polarization degree of around 30$\,\%$, constant during the
initial sub-picosecond decay, followed by the depolarization on a picosecond
timescale. The FWM hyperspectral imaging reveals the doped and undoped areas of
the sample, allowing to investigate the neutral exciton, the charged one or
both transitions at the same time. In the latter case, we observe the
exciton-trion beating in the coherence evolution indicating their coherent
coupling.
