  Stellar radiation from X-rays to the visible provides the energy that
controls the photochemistry and mass loss from exoplanet atmospheres. The
important extreme ultraviolet (EUV) region (10--91.2~nm) is inaccessible and
should be computed from a reliable stellar model. It is essential to understand
the formation regions and physical processes responsible for the various
stellar emission features in order to predict how the spectral energy
distribution varies with age and activity levels. We compute a state-of-the-art
semi-empirical atmospheric model and the emergent high-resolution synthetic
spectrum of the moderately active M2~V star GJ~832 as the first of a series of
models for stars with different activity levels. Using non-LTE radiative
transfer techniques and including many molecular lines, we construct a
one-dimensional simple model for the physical structure of the star's
chromosphere, chromosphere-corona transition region, and corona. The
synthesized spectrum for this model fits the continuum and lines across the UV
to optical spectrum. Particular emphasis is given to the emission lines at
wavelengths shorter than 300~nm observed with {\em HST}, which have important
effects on the photochemistry in the exoplanet atmospheres. The FUV line ratios
indicate that the transition region of GJ~832 is more biased to hotter material
than that of the quiet Sun. The excellent agreement of our computed EUV
luminosity with that obtained by two other techniques indicates that our model
predicts reliable EUV emission from GJ~832. We find that unobserved EUV flux of
GJ~832, which heats the outer atmospheres of exoplanets and drives their mass
loss, is comparable to the active Sun.
