We propose to determine the distribution of warm molecular gas in a variety of Galactic sources. Using the SWS, we will partially map the emission in the 0-0 S(1) and S(5) lines of the hydrogen molecule in sources which have strong shocked or fluorescent near-IR H2 line emission. This allows us to study a regime of parameter space, warm molecular gas at 100-200K, for the first time with a probe arising from the bulk of the gas present, a ground state transition of the hydrogen molecule. At temperatures as low as 100K the 0-0 S(1) line is the strongest line of H2, and considerably easier to observe than the 0-0 S(0) line. Much of the gas in molecular clouds, outside of dense cores, is at these temperatures. It is in the form of PDRs, heated by the ambient interstellar radiation field. We predict detectable levels of 0-0 S(1) line emission from PDRs. The shock-excited emission from the 0-0 S(1) line is also predicted to be more extensive than the near-IR lines, as it can be excited in lower velocity shocks, down to ~5 km/s, than the higher excitation lines. In addition, the ratio of the 0-0 and 1-0 S(1) lines depends sensitively on the shock model and the environment of the cloud, and thus will provide a diagnostic to test competing models. Since comprehensive mapping is impracticable, our strategy is to make partial maps of a number of different types of source, concentrating on the brightest peaks of H2 emission, making cross cuts along and across ridges of emission, and observing where we have KAO data on other tracers, such as OI and CII. We will combine these data with an extensive data base on near-IR H2 lines we have collected, and with models of the H2 emission in shocks and PDRs we have constructed, to build a picture of the excitation of molecular hydrogen across the entire energy spectrum of the ground electronic state. We seek particularly to test out the viability of a bow C-shock model for molecular shocks, and to determine whether molecular hydrogen is the dominant coolant in the lower (T < 1000K) gas downstream of the front.