Abstract: We propose to launch the first extreme-ultraviolet (EUV) space science mission in China to explore the sources of space weather both within and beyond the solar system, specifically the solar and stellar coronae. The primary scientific objects of this mission, Coronal Explorer for our Sun and nearby Stars (CESS), are as follows: (1) Characterize the physical properties of the source regions of solar coronal outflows and eruptions through full-disk EUV spectroscopy of the Sun; (2) Detect stellar coronal eruptions through long-term EUV photometric and spectroscopic monitoring of the coronae of selected nearby late-type stars; (3) Explore the role of space weather in the formation of a habitable world through point-source EUV observations of the Sun and other stars. To fulfill these scientific goals, the spacecraft will be equipped with four key science payloads: an EUV solar-disk spectrometer (comprising a Sun-as-a-star spectrometer and a multi-slit spectrometer with a full-disk field of view), an EUV spectroscopic coronagraph, a stellar EUV spectrometer and a stellar EUV photometer. The CESS mission will contribute to the precise prediction of space weather in the solar system, uncover the origin of exoplanetary space weather, and offer crucial clues for the search for extraterrestrial life.