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We report the results from spectroscopic observations of the multiple imagesof the strongly lensed Type Ia supernova (SN Ia), iPTF16geu, obtained withground based telescopes and the Hubble Space Telescope (HST). From a singleepoch of slitless spectroscopy with HST, we can resolve spectra of individuallensed supernova images for the first time. This allows us to perform anindependent measurement of the time-delay between the two brightest images,$\Delta t = 1.4 \pm 5.0$ days, which is consistent with the time-delay measuredfrom the light-curves.  We also present measurements of narrow emission and absorption linescharacterizing the interstellar medium in the host galaxy at z=0.4087, as wellas in the foreground lensing galaxy at z=0.2163. We detect strong Na IDabsorption in the host galaxy, indicating that iPTF16geu belongs to a subclassof SNe Ia displaying "anomalously" large Na ID column densities in comparisonto the amount of dust extinction derived from their light curves. For thedeflecting galaxy, we refine the measurement of the velocity dispersion,$\sigma = 129 \pm 4$ km/s, which significantly constrains the lens model.  Since the time-delay between the SN images is negligible, we can useunresolved ground based spectroscopy, boosted by a factor ~70 from lensingmagnification, to study the properties of a high-z SN Ia with unprecedentedsignal-to-noise ratio. The spectral properties of the supernova, such aspseudo-Equivalent widths of several absorption features and velocities of theSi II-line indicate that iPTF16geu, besides being lensed, is a normal SN Ia,indistinguishable from well-studied ones in the local universe, providingsupport for the use of SNe Ia in precision cosmology. We do not detect anysignificant deviations of the SN spectral energy distribution from microlensingof the SN photosphere by stars and compact objects in the lensing galaxy.

Spectroscopy of the first resolved strongly lensed Type Ia supernova iPTF16geu