We present the results of a program to map the Sh2-235 molecular cloud complex in the CO and (CO)-C-13 J = 2 - 1 transitions using the Heinrich Hertz Submillimeter Telescope. The map resolution is 38 '' (FWHM), with an rms noise of 0.12K brightness temperature, for a velocity resolution of 0.34 km s(-1). With the same telescope, we also mapped the CO J = 3 - 2 line at a frequency of 345 GHz, using a 64 beam focal plane array of heterodyne mixers, achieving a typical rms noise of 0.5 K brightness temperature with a velocity resolution of 0.23 km s(-1). The three spectral line data cubes are available for download. Much of the cloud appears to be slightly sub-thermally excited in the J = 3 level, except for in the vicinity of the warmest and highest column density areas, which are currently forming stars. Using the CO and (CO)-C-13. J = 2 - 1 lines, we employ an LTE model to derive the gas column density over the entire mapped region. Examining a 125 pc(2). region centered on the most active star formation in the vicinity of Sh2-235, we find that the young stellar object surface density scales as approximately the 1.6-power of the gas column density. The area distribution function of the gas is a steeply declining exponential function of gas column density. Comparison of the morphology of ionized and molecular gas suggests that the cloud is being substantially disrupted by expansion of the H II regions, which may be triggering current star formation.