  We present the far-ultraviolet (FUV) fluorescent molecular hydrogen (H_2)
emission map of the Milky Way Galaxy obtained with FIMS/SPEAR covering ~76% of
the sky. The extinction-corrected intensity of the fluorescent H_2 emission has
a strong linear correlation with the well-known tracers of the cold
interstellar medium (ISM), including color excess E(B-V), neutral hydrogen
column density N(H I), and H_alpha emission. The all-sky H_2 column density map
was also obtained using a simple photodissociation region model and
interstellar radiation fields derived from UV star catalogs. We estimated the
fraction of H2 (f_H2) and the gas-to-dust ratio (GDR) of the diffuse ISM. The
f_H2 gradually increases from <1% at optically thin regions where E(B-V) < 0.1
to ~50% for E(B-V) = 3. The estimated GDR is ~5.1 x 10^21 atoms cm^-2 mag^-1,
in agreement with the standard value of 5.8 x 10^21 atoms cm^-2 mag^-1.
