We present the results of spectroscopic studies with the LRIS spectrograph on Keck of two of the Hawaii deep survey fields. The 393 objects observed cover an area of 26.2 square arcmin and constitute a nearly complete sample down to K = 20, I = 23, and B = 24.5. The rest-frame K-band luminosity function and its evolution with redshift are described. Comparisons are made with other optically selected (B and I) samples in the literature, and the corresponding rest-frame B-band luminosity function evolution is presented. The B-band counts near B = 24 are shown to be a mixture of normal galaxies at modest redshifts and galaxies undergoing rapid star formation, which have a wide range of masses and which are spread over the redshift interval from z = 0.2 to beyond z = 1.7. The luminosity functions, number counts, and color distributions at optical and IR wavelengths are discussed in terms of a consistent picture of the star-forming history of the galaxy sample. [OII] emission-line diagnostics or rest-frame ultra-violet--infrared color information are used in combination with rest-frame absolute K magnitudes to construct a ``fundamental plane'' in which the evolution of the global star-formation rate with redshift can be shown, and we find that the maximum rest-frame K luminosity of galaxies undergoing rapid star formation has been declining smoothly with decreasing redshift from a value near L* at z > 1. This smooth decrease in the characteristic luminosity of galaxies dominated by star formation can simultaneously account for the high B-band galaxy counts at faint magnitudes and the redshift distribution at z < 1 in both the B- and K-selected samples. Finally, the overall K-band light density evolution is discussed as a tracer of the baryonic mass in stars and compared with the rate of star formation.Comment: 38 pages plus 2 tables, 28 Postscript figures, Figure 1 (finding charts) and Figure 2 (sample spectra) available at http://galileo.ifa.hawaii.edu/~cowie/insight.html . To be published in Astronomical Journal (9/96