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.
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