  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.
