Aims: The spatial structure of the emission lines and continuum over the 50″ extent of the nearby, O-rich, PN NGC 7009 (Saturn Nebula) have been observed with the MUSE integral field spectrograph on the ESO Very Large Telescope. This study concentrates on maps of line emission and their interpretation in terms of physical conditions. Methods: MUSE Science Verification data, in <0.6″ seeing, have been reduced and analysed as maps of emission lines and continuum over the wavelength range 4750-9350 Å. The dust extinction, the electron densities and temperatures of various phases of the ionized gas, abundances of species from low to high ionization and some total abundances are determined using standard techniques. Results: Emission line maps over the bright shells are presented, from neutral to the highest ionization available (He II and [Mn V]). For collisionally excited lines (CELs), maps of electron temperature (Te from [N II] and [S III]) and density (Ne from [S II] and [Cl III]) are available and for optical recombination lines (ORLs) temperature (from the Paschen jump and ratio of He I lines) and density (from high Paschen lines). These estimates are compared: for the first time, maps of the differences in CEL and ORL Te's have been derived, and correspondingly a map of t2 between a CEL and ORL temperature, showing considerable detail. Total abundances of only He and O were formed, the latter using three ionization correction factors. However, the map of He/H is not flat, departing by 2% from a constant value, with remnants corresponding to ionization structures. An integrated spectrum over an area of 2340 arcsec2 was also formed and compared to 1D photoionization models. Conclusions: The spatial variation of a range of nebular parameters illustrates the complexity of the ionized media in NGC 7009. These MUSE data are very rich with detections of hundreds of lines over areas of hundreds of arcsec2 and follow-on studies are outlined. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile in Science Verification (SV) observing proposal 60.A-9347(A).FITS files of all the individual maps are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/620/A169