This is the Science Case document of the TARSIS instrumental project for the Calar Alto 3.5m telescope. The main science driver of the instrument is the CATARSIS survey. CATARSIS, the Calar Alto Tetra-Armed Super-IFu spectrograph Survey, will survey ~16 galaxy clusters in the redshift range 0.15 < z < 0.23 to understand the formation of structures and the evolution of galaxies in a dynamic and growing environment. CATARSIS will sample each cluster from the center to 2xR200, obtaining 2D spectra in the TARSIS full spectral range (320-810 nm) of all the targets brighter than mr,AB = 22 mag and galaxies with even fainter magnitudes but with emission line fluxes above 1-2 x 10−17 erg s−1 cm−2. TARSIS (Tetra-ARm Spectrograph for the Imaging Survey) is a wide-field, optical multi-arm spectrograph being developed for the 3.5 m Calar Alto telescope, designed to deliver low-to-mid resolution spectroscopy over a very large field of view using a four-quadrants IFU that are adjacent on the sky. The IFU splits the light into four optimized spectral arms (one per quadrant), one in the UV-blue (from 320-520nm) and three in the red (510-810nm). TARSIS is conceived primarily to conduct large spectroscopic surveys — for example, mapping galaxy clusters, intracluster light, and the cosmic web —, especially the CATARISIS survey outlined above, but its flexible design also supports a broad range of extragalactic and Galactic science cases that benefit from efficient, wide-field optical spectroscopy.