We report results from a FUSE survey of interstellar molecular hydrogen (H2) along 45 sight lines to AGN at high Galactic latitudes (|b| > 20 degrees). Most (39 of 45) of the sight lines show detectable Galactic H2 absorption from Lyman and Werner bands between 1000 and 1126 A, with column densities ranging from N(H2) = 10^(14.17-19.82) cm^-2. In the northern Galactic hemisphere, we identify many regions of low column, N(H2) < 10^15 cm^-2, between longitude l = 60-180 degrees and at b > 54 degrees. These `H2 holes provide valuable, uncontaminated sight lines for extragalactic UV spectroscopy, and a few may be related to the Northern Chimney (low Na I absorption) and Lockman Hole with low N(HI). A comparison of high-latitude H2 with 139 OB-star sight lines surveyed in the Galactic disk suggests that high-latitude and disk H2 clouds may have different rates of heating, cooling, and UV excitation. For rotational states J = 0 and 1, the mean excitation temperature at high latitude, <T_01(high)> = 124 +/- 8 K, is somewhat above that in the Galactic disk, <T_01(disk)> = 86 +/- 20 K. For J = 2-4, the <T_exc> = 498 +/- 28 K, and the column-density ratios, N(3)/N(1), N(4)/N(0), and N(4)/N(2), indicate a comparable degree of UV excitation in the disk and low halo for sight lines with N(H2) > 10^18. The distribution of molecular fractions at high latitude shows a transition at lower total hydrogen column density, log N_H = 20.38 +/- 0.13, than in the Galactic disk, log N_H(disk) = 20.7. If the FUV radiation fields are similar in disk and low halo, this suggests an enhanced (dust-catalyzed) H2 formation rate in higher-density, compressed clouds, which could be detectable as high-latitude, sheetlike infrared cirrus.
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