Context :

Aims:2D spectroscopic data for the whole extent of the NGC 3132 planetary nebula have been obtained .
We deliver a reduced data-cube and high-quality maps on a spaxel-by-spaxel basis for the many emission lines falling within the MUSE spectral coverage over a range in surface brightness > 1000 .
Physical diagnostics derived from the emission line images , opening up a variety of scientific applications , are discussed .

Methods : Data were obtained during MUSE commissioning on the ESO Very Large Telescope and reduced with the standard ESO pipeline .
Emission lines were fitted by Gaussian profiles .
The dust extinction , electron densities and temperatures of the ionised gas and abundances were determined using Python and PyNeb routines .

Results : The delivered datacube has a spatial size of \sim 63 ^ { \prime \prime } \times 123 ^ { \prime \prime } , corresponding to \sim 0.26 \times 0.51 pc ^ { 2 } for the adopted distance , and a contiguous wavelength coverage of 4750-9300 Å at a spectral sampling of 1.25 Å pix ^ { -1 } .
The nebula presents a complex reddening structure with high values ( c ( H \beta ) \sim 0.4 ) at the rim .
Density maps are compatible with an inner high-ionisation plasma at moderate high density ( \sim 1000 cm ^ { -3 } ) while the low-ionisation plasma presents a structure in density peaking at the rim with values \sim 700 cm ^ { -3 } .
Median T _ { e } using different diagnostics decreases according to the sequence [ N ii ] , [ S ii ] \rightarrow [ S iii ] \rightarrow [ O i ] \rightarrow He i \rightarrow Paschen Jump .
Likewise the range of temperatures covered by recombination lines is much larger than those obtained from collisionally excited lines ( CELs ) , with large spatial variations within the nebula .
If these differences were due to the existence of high density clumps , as previously suggested , these spatial variations suggest changes in the properties and/or distribution of the clumps within the nebula .
We determined a median helium abundance He / H = 0.124 , with slightly higher values at the rim and outer shell .
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 .
Specifically , our derived velocity maps support a geometry for the nebula similar to the diabolo-like model proposed by \citet Monteiro00 , but oriented with its major axis roughly at P.A . \sim - 22 ^ { \circ } .
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 .
A simple 1D Cloudy model is able to reproduce the strong lines in the integrated spectrum of the whole nebula with an accuracy of \sim 15 % .

Conclusions : Together with the work on NGC 7009 presented by \citet Walsh18 , the present study illustrates the enormous potential of wide field integral field spectrographs for the study of Galactic PNe .