GravityCam is a new concept of ground-based imaging instrument capable of delivering significantly sharper images from the ground than is normally possible without adaptive optics. Advances in optical and near-infrared imaging technologies allow images to be acquired at high speed without significant noise penalty. Aligning these images before they are combined can yield a 2.5-3-fold improvement in image resolution. By using arrays of such detectors, survey fields may be as wide as the telescope optics allows. Consequently, GravityCam enables both wide-field high-resolution imaging and high-speed photometry. We describe the instrument and detail its application to provide demographics of planets and satellites down to Lunar mass (or even below) across the Milky Way. GravityCam is also suited to improve the quality of weak shear studies of dark matter distribution in distant clusters of galaxies and multiwavelength follow-ups of background sources that are strongly lensed by galaxy clusters. The photometric data arising from an extensive microlensing survey will also be useful for asteroseismology studies, while GravityCam can be used to monitor fast multiwavelength flaring in accreting compact objects and promises to generate a unique data set on the population of the Kuiper belt and possibly the Oort cloud.