  The study of non-thermal processes such as synchrotron emission, inverse
Compton scattering, bremsstrahlung and pion production is crucial to understand
the properties of the Galactic cosmic-ray population, to shed light on their
origin and confinement mechanisms, and to assess the significance of exotic
signals possibly associated to new physics. We present a public code called
HERMES aimed at generating sky maps associated to a variety of multi-messenger
and multi-wavelength radiative processes, spanning from the radio domain all
the way up to high-energy gamma-ray and neutrino production. We describe the
physical processes under consideration, the code concept and structure, and the
user interface, with particular focus on the python-based interactive mode. We
especially present the modular and flexible design that allows to easily
further extend the numerical package according to the user's needs. In order to
demonstrate the capabilities of the code, we describe in detail a comprehensive
set of sky maps and spectra associated to all physical processes included in
the code. We comment in particular on the radio, gamma-ray, and neutrino maps,
and mention the possibility to study signals stemming from dark matter
annihilation. HERMES can be successfully applied to constrain the properties of
the Galactic cosmic-ray population, improve our understanding of the diffuse
Galactic radio, gamma--ray, and neutrino emission, and search for signals
associated to particle dark matter annihilation or decay.
