  We present a large VLT/MUSE mosaic (3.8 x 3.8 kpc) of the nearby spiral
galaxy M83, with a spatial resolution ~20 pc. We obtained the kinematics of the
stars and ionised gas, and compared them with molecular gas kinematics from
ALMA CO(2-1). We separated the ionised gas into HII regions and diffuse ionised
gas (DIG) and determined the fraction of Ha luminosity originating from the DIG
(f_DIG). We observe that both stars and gas trace the galactic disk rotation,
as well as a fast-rotating nuclear component, likely connected to secular
processes driven by the galactic bar. In the gas kinematics, we observe a
stream east of the nucleus, redshifted with respect to the disk. The stream is
surrounded by an extended ionised gas region with enhanced velocity dispersion
and a high ionisation state, which is largely consistent with being ionised by
slow shocks. We interpret this feature as either the superposition of the disk
and an extraplanar layer of DIG, or as a bar-driven inflow of shocked gas. A
double Gaussian component fit to the Ha line also reveals the presence of a
nuclear biconic structure whose axis of symmetry is perpendicular to the bar.
The two cones appear blue- and redshifted along the line of sight and stand out
for having an Ha emission separated by up to 200 km s-1 from that of the disk,
and a high velocity dispersion ~80-200 km s-1. At the far end of the cones, we
observe that the gas is consistent with being ionised by shocks. These features
had never been observed before in M83; we postulate that they are tracing a
starburst-driven outflow shocking into the surrounding ISM. Finally, we obtain
f_DIG ~ 13% in our field of view. We inspect the emission of the HII regions
and DIG in `BPT' diagrams, finding that in HII regions photoionisation accounts
for 99.8% of the Ha flux, whereas the DIG has a mixed contribution from
photoionisation (94.9%) and shocks (5.1%). [abridged]
