  We present 21-cm Spectral Line Observations of Neutral Gas with the VLA
(21-SPONGE), a Karl G. Jansky Very Large Array (VLA) large project (~600 hours)
for measuring the physical properties of Galactic neutral hydrogen (HI).
21-SPONGE is distinguished among previous Galactic HI studies as a result of:
(1) exceptional optical depth sensitivity ($\sigma_{\tau} < 10^{-3}$ per
$0.42\rm\,km\,s^{-1}$ channels over 57 lines of sight); (2) matching 21 cm
emission spectra with highest-possible angular resolution (~4') from the
Arecibo Observatory; (3) detailed comparisons with numerical simulations for
assessing observational biases. We autonomously decompose 21 cm spectra and
derive the physical properties (i.e., spin temperature, $T_s$, column density)
of the cold neutral medium (CNM; $T_s<250\rm\,K$), thermally unstable medium
(UNM; $250< T_s < 1000\rm\,K$) and warm neutral medium (WNM; $T_s >
1000\rm\,K$) simultaneously. We detect 50% of the total HI mass in absorption,
the majority of which is CNM (56 +/- 10%, corresponding to 28% of the total HI
mass). Although CNM is detected ubiquitously, the CNM fraction along most lines
of sight is <50%. We find that 20% of the total HI mass is thermally unstable
(41 +/- 10% of HI detected in absorption), with no significant variation with
Galactic environment. Finally, although the WNM comprises 52% of the total HI
mass, we detect little evidence for WNM absorption with $1000<T_s<4000\rm\,K$.
Following spectral modeling, we detect a stacked residual absorption feature
corresponding to WNM with $T_s\sim10^4\rm\,K$. We conclude that excitation in
excess of collisions likely produces significantly higher WNM $T_s$ than
predicted by steady-state models.
