MAORY is the Adaptive Optic (AO) module that will be installed at the E-ELT at the first light of the telescope. It will provide two different types of AO correction, a very high correction over a small FoV (diameter ~10 arcsec, SCAO mode) and a moderate and homogeneous correction over a wide FoV (diameter ~60 arcsec, MCAO mode). Here we present a first collection of science cases for MAORY feeding the E-ELT first light camera and spectrograph MICADO. Since the general science cases for E-ELT have already been developed elsewhere, here we focus on the design of specific observations, to explore the capabilities and observing modes of the system.