  We estimate energy spectra and fluxes at the Earth's surface of the cosmic
and Galactic neutrino backgrounds produced by thermonuclear reactions in stars.
The extra-galactic component is obtained by combining the most recent estimates
of the cosmic star formation history and the stellar initial mass function with
accurate theoretical predictions of the neutrino yields all over the
thermonuclear lifetime of stars of different masses. Models of the structure
and evolution of the Milky Way are used to derive maps of the expected flux
generated by Galactic sources as a function of sky direction. The predicted
neutrino backgrounds depend only slightly on model parameters. In the relevant
50 keV-10 MeV window, the total flux of cosmic neutrinos ranges between 20 and
65 particles per square cm per s. Neutrinos reaching the Earth today have been
typically emitted at redshift z~2. Their energy spectrum peaks at E~0.1-0.3
MeV. The energy and entropy densities of the cosmic background are negligible
with respect to the thermal contribution of relic neutrinos originated in the
early universe. In every sky direction, the cosmic background is outnumbered by
the Galactic one, whose integrated flux amounts to 300-1000 particles per
square cm per s. The emission from stars in the Galactic disk contributes more
than 95 per cent of the signal.
