The chemical evolution of fluorine is investigated in a sample of Milky Way red giantstars that span a significant range in metallicity from [Fe/H] $sim$ -1.3 to 0.0 dex. Fluorine abundances are derived from vibration-rotation lines of HF in high-resolution infraredspectra near $lambda$ 2.335 $mu$m. The red giants are members of the thin and thick disk / halo,with two stars being likely members of the outer disk Monoceros overdensity. At lowermetallicities, with [Fe/H]<-0.4 to -0.5, the abundance of F varies as a primary element with respect to the Fe abundance, with a constant subsolar value of [F/Fe] $sim$ -0.3 to -0.4 dex. At larger metallicities, however, [F/Fe] increases rapidly with [Fe/H] anddisplays a near-secondary behavior with respect to Fe. Comparisons with various models of chemical evolution suggest that in the low-metallicity regime (dominated hereby thick disk stars), a primary evolution of $^{19}$F with Fe, with a subsolar [F/Fe] valuethat roughly matches the observed plateau can be reproduced by a model incorporatingneutrino nucleosynthesis in the aftermath of the core collapse in supernovae of type II (SN II). A primary behavior for [F/Fe] at low metallicity is also observed for a model including rapid rotating low-metallicity massive stars but this overproduces [F/Fe] atlow metallicity. The thick disk red giants in our sample span a large range of galactocentric distance (Rg $sim$ 6--13.7 kpc), yet display a $sim$constant value of [F/Fe], indicating a very flat gradient (with a slope of 0.02 $pm$ 0.03 dex/kpc) of this elemental ratio over asignificant portion of the Galaxy having|Z|>300 pc away from the Galaxy mid-plane.
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