  We present MUSE observations in the core of the HFF galaxy cluster MACS
J1149.5+2223, where the first magnified and spatially-resolved multiple images
of SN 'Refsdal' at redshift 1.489 were detected. Thanks to a DDT program with
the VLT and the extraordinary efficiency of MUSE, we measure 117 secure
redshifts with just 4.8 hours of total integration time on a single target
pointing. We spectroscopically confirm 68 galaxy cluster members, with redshift
values ranging from 0.5272 to 0.5660, and 18 multiple images belonging to 7
background, lensed sources distributed in redshifts between 1.240 and 3.703.
Starting from the combination of our catalog with those obtained from extensive
spectroscopic and photometric campaigns using the HST, we select a sample of
300 (164 spectroscopic and 136 photometric) cluster members, within
approximately 500 kpc from the BCG, and a set of 88 reliable multiple images
associated to 10 different background source galaxies and 18 distinct knots in
the spiral galaxy hosting SN 'Refsdal'. We exploit this valuable information to
build 6 detailed strong lensing models, the best of which reproduces the
observed positions of the multiple images with a rms offset of only 0.26". We
use these models to quantify the statistical and systematic errors on the
predicted values of magnification and time delay of the next emerging image of
SN 'Refsdal'. We find that its peak luminosity should should occur between
March and June 2016, and should be approximately 20% fainter than the dimmest
(S4) of the previously detected images but above the detection limit of the
planned HST/WFC3 follow-up. We present our two-dimensional reconstruction of
the cluster mass density distribution and of the SN 'Refsdal' host galaxy
surface brightness distribution. We outline the roadmap towards even better
strong lensing models with a synergetic MUSE and HST effort.
