We present the Phase A Science Case for the Multi-conjugate Adaptive-optics Visible Imager-Spectrograph (MAVIS), planned for the Adaptive Optics Facility (AOF) of the Very Large Telescope (VLT). MAVIS is a general-purpose instrument for exploiting the highest possible angular resolution of any single optical telescope available in the next decade, either on Earth or in space, and with sensitivity comparable to (or better than) larger aperture facilities. MAVIS uses two deformable mirrors in addition to the deformable secondary mirror of the AOF, providing a mean V-band Strehl ratio of >10% (goal >15%) across a relatively large (30 arc second) science field. This equates to a resolution of <20mas at 550nm - comparable to the K-band diffraction limit of the next generation of extremely large telescopes, making MAVIS a genuine optical counterpart to future IR-optimised facilities like JWST and the ELT. Moreover, MAVIS will have unprecedented sky coverage for a high-order AO system, accessing at least 50% of the sky at the Galactic Pole, making MAVIS a truly general purpose facility instrument. As such, MAVIS will have both a Nyquist-sampled imager (30x30 arcsec field), and a powerful integral field spectrograph with multiple spatial and spectral modes spanning 370-1000nm. This science case presents a distilled set of thematically linked science cases drawn from the MAVIS White Papers (www.mavis-ao.org/whitepapers), selected to illustrate the driving requirements of the instrument resulting from the recent MAVIS Phase A study.
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