  We present the consolidated scientific case for multi-object spectroscopy
with the MOSAIC concept on the European ELT. The cases span the full range of
ELT science and require either 'high multiplex' or 'high definition'
observations to best exploit the excellent sensitivity and wide field-of-view
of the telescope. Following scientific prioritisation by the Science Team
during the recent Phase A study of the MOSAIC concept, we highlight four key
surveys designed for the instrument using detailed simulations of its
scientific performance. We discuss future ways to optimise the conceptual
design of MOSAIC in Phase B, and illustrate its competitiveness and unique
capabilities by comparison with other facilities that will be available in the
2020s.
