We report the results from spectroscopic observations of the multiple images of the strongly lensed Type Ia supernova ( SN Ia ) , iPTF16geu , obtained with ground based telescopes and the Hubble Space Telescope ( HST ) . From a single epoch of slitless spectroscopy with HST , we can resolve spectra of individual lensed supernova images for the first time . This allows us to perform an independent 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 measured from the light-curves . We also present measurements of narrow emission and absorption lines characterizing the interstellar medium in the SN Ia host galaxy at z = 0.4087 , as well as in the foreground lensing galaxy at z = 0.2163 . We detect strong \ion Naid absorption in the host galaxy , indicating that iPTF16geu belongs to a subclass of SNe Ia displaying `` anomalously '' large \ion Naid column densities in comparison to the amount of dust extinction derived from their light curves . For the deflecting galaxy , we refine the measurement of the velocity dispersion , \sigma = 129 \pm 4 km s ^ { -1 } , which significantly constrains the lens model . Since the time-delay between the SN images is negligible , we can use unresolved ground based spectroscopy , boosted by a factor \sim 70 from lensing magnification , to study the properties of a high- z SN Ia with unprecedented signal-to-noise ratio . The spectral properties of the supernova , such as pseudo-Equivalent widths of several absorption features and velocities of the \ion Siii-line indicate that iPTF16geu , besides being lensed , is a normal SN Ia , indistinguishable from well-studied ones in the local universe , providing support for the use of SNe Ia in precision cosmology . We do not detect any significant deviations of the SN spectral energy distribution from microlensing of the SN photosphere by stars and compact objects in the lensing galaxy .