  ABRIDGED: 2D spectroscopic MUSE data for the whole extent of NGC3132 have
been reduced and analised. The dust extinction, electron densities and
temperatures of the ionised gas and abundances were determined. The nebula
presents a complex reddening structure with high values (c(Hb)~0.4) at the rim.
Density maps are compatible with an inner high-ionisation plasma at moderate
high density (~1000cm^-3) while the low-ionisation plasma presents a structure
in density peaking at the rim with values ~700 cm^-3. Median Te using different
diagnostics decreases according to the sequence
[NII],[SII]->[SIII]->[OI]->HeI->PJ. Likewise the range of Te covered by
recombination lines is much larger than those obtained from CELs, with large
spatial variations within the nebula. If these differences were due to the
existence of high density clumps, these spatial variations suggest changes in
the properties and/or distribution of the clumps within the nebula. We
determined a median He/H=0.124. The range of measured ionic abundances for
light elements are compatible with literature values. Our kinematic analysis
nicely illustrates the power of 2D kinematic information in many emission lines
to shed light on the intrinsic structure of the nebula. Our derived velocity
maps support a geometry for the nebula similar to the previously propose
diabolo model, but oriented with its major axis at P.A.~-22^o. We identified
two low-surface brightness arc-like structures towards the northern and
southern tips of the nebula, with high extinction, high helium abundance, and
strong low-ionisation emission lines. They are spatially coincident with some
extended low-surface brightness mid-IR emission. The characteristics of the
features are compatible with being the consequence of precessing jets caused by
the binary star system. This study illustrates the enormous potential of IFS
for the study of Galactic PNe.
