The long-term stability of exoplanetary atmospheres depends critically on the extreme-ultraviolet (EUV) flux from the host star. The EUV flux likely controls the demographics of the short-period planet population as well the ability for rocky planets to maintain habitable environments long enough for the emergence of life. We present the Extreme-ultraviolet Stellar Characterization for Atmospheric Physics and Evolution (ESCAPE) mission, an astrophysics Small Explorer proposed to NASA. ESCAPE employs extreme- and far-ultraviolet spectroscopy (70 - 1800 Α) to characterize the highenergy radiation environment in the habitable zones (HZs) around nearby stars. ESCAPE provides the first comprehensive study of the stellar EUV environments that control atmospheric mass-loss and determine the habitability of rocky exoplanets. The ESCAPE instrument comprises an EUV grazing incidence telescope feeding four diffraction gratings and a photon-counting detector. The telescope is 50 cm diameter with four nested parabolic primary mirrors and four nested elliptical secondary mirrors, fabricated and aligned by NASA Marshall Space Flight Center and the Smithsonian Astrophysical Observatory. The off-plane grating assemblies are fabricated at Pennsylvania State University and the ESCAPE detector system is a micro-channel plate (MCP; 125mm x 40mm active area) sensor developed by the University of California, Berkeley. ESCAPE employs the versatile and high-heritage Ball Aerospace BCP-100 spacecraft.