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We introduce VLT-MUSE observations of the central 2$'\times2'$ (30$\times$30pc) of the Tarantula Nebula in the Large Magellanic Cloud. The observationsprovide an unprecedented spectroscopic census of the massive stars and ionisedgas in the vicinity of R136, the young, dense star cluster located in NGC 2070,at the heart of the richest star-forming region in the Local Group.Spectrophotometry and radial-velocity estimates of the nebular gas(superimposed on the stellar spectra) are provided for 2255 point sourcesextracted from the MUSE datacubes, and we present estimates of stellar radialvelocities for 270 early-type stars (finding an average systemic velocity of271$\pm$41 km/s). We present an extinction map constructed from the nebularBalmer lines, with electron densities and temperatures estimated from intensityratios of the [SII], [NII], and [SIII] lines. The interstellar medium, astraced by H$\alpha$ and [NII] $\lambda$6583, provides new insights in regionswhere stars are probably forming. The gas kinematics are complex, but with aclear bi-modal, blue- and red-shifted distribution compared to the systemicvelocity of the gas centred on R136. Interesting point-like sources are alsoseen in the eastern cavity, western shell, and around R136; these might berelated to phenomena such as runaway stars, jets, formation of new stars, orthe interaction of the gas with the population of Wolf--Rayet stars. Closerinspection of the core reveals red-shifted material surrounding the strongestX-ray sources, although we are unable to investigate the kinematics in detailas the stars are spatially unresolved in the MUSE data. Further papers in thisseries will discuss the detailed stellar content of NGC 2070 and its integratedstellar and nebular properties.

Mapping the core of the Tarantula Nebula with VLT-MUSE: I. Spectral and nebular content around R136