Probing of Hermean exosphere by ultraviolet spectroscopy (PHEBUS) is a double spectrometer for the Extreme Ultraviolet range (55-155 nm) and the Far Ultraviolet range (145-315 nm) devoted to the characterization of Mercury's exosphere composition and dynamics, and surface-exosphere connections. This French-led instrument is implemented in a cooperative scheme involving Japan (detectors), Russia (scanner) and Italy (ground calibration). PHEBUS will address the following main scientific objectives relative to Mercury's exosphere: determination of the composition and the vertical structure of the exosphere; characterization of the exospheric dynamics: day to night circulation, transport between active and inactive regions; study of surface release processes; identification and characterization of the sources of exospheric constituents; detection and characterization of ionized species and their relation with the neutral atmosphere; space and time monitoring of exosphere/magnetosphere exchange and transport processes; study and quantification of escape, global scale source/sink balance and geochemical cycles synergistically with other experiments of BepiColombo (Mercury Sodium Atmospheric Spectral Imager (MSASI), Mercury Plasma Particle Experiment (MPPE) on Mercury Magnetospheric Orbiter (MMO); Mercury imaging X-ray spectrometer (MIXS), Search for exosphere refilling and emitted neutral abundance (SERENA) on Mercury Planetary Orbiter (MPO)). Two gratings and two detectors are used according to a specific, compact design. The spectrum detection is based on the photon counting method and is realized using micro-channel plate (MCP) detectors with Resistive Anode Encoder (RAE). Typical photocathodes are CsI or KBr for the extreme ultra-violet (EUV) range, CsTe for the far ultra-violet (FUV) range. Extra visible lines are monitored using a photo-multiplier (PM) that is also used in photon counting mode. In order to prevent sensitivity losses which are critical in UV ranges, a minimum of reflections is achieved inside the instrument using only an off-axis parabola and a set of holographic gratings. A one degree-of-freedom scanning system allows to probe, at the highest possible signal-to-noise ratio, selected regions and altitude ranges of interest. Different modes of observation will be used sequentially (vertical scans, along-orbit scans, grazing observations at twilight, etc.). During the mission, the instrument will be regularly calibrated on well chosen stars, in such a way to quantitatively estimate the overall degradation of the sensitivity of the instrument.