We present galaxy luminosity functions at 3.6, 4.5, 5.8, and 8.0 μm measured by combining photometry from the IRAC Shallow Survey with redshifts from the AGN and Galaxy Evolution Survey (AGES) of the NOAO Deep Wide-Field Survey Boötes field. The well defined IRAC samples contain 3800-5800 galaxies for the 3.6-8.0 μm bands with spectroscopic redshifts and z < 0.6. We obtained relatively complete luminosity functions in the local redshift bin of z < 0.2 for all four IRAC channels that are well fitted by Schechter functions. After analyzing the samples for the whole redshift range, we found significant evolution in the luminosity functions for all four IRAC channels that can be fitted as an evolution in M * with redshift, ΔM * = Qz. While we measured Q = 1.2 ± 0.4 and 1.1 ± 0.4 in the 3.6 and 4.5 μm bands consistent with the predictions from a passively evolving population, we obtained Q = 1.8 ± 1.1 in the 8.0 μm band consistent with other evolving star formation rate estimates. We compared our luminosity functions with the predictions of semianalytical galaxy formation and found the best agreement at 3.6 and 4.5 μm, rough agreement at 8.0 μm, and a large mismatch at 5.8 μm. These models also predicted a comparable Q-value to our luminosity functions at 8.0 μm, but predicted smaller values at 3.6 and 4.5 μm. We also measured the luminosity functions separately for early- and late-type galaxies. While the luminosity functions of late-type galaxies resemble those for the total population, the luminosity functions of early-type galaxies in the 3.6 and 4.5 μm bands indicate deviations from the passive evolution model, especially from the measured flat luminosity density evolution. Combining our estimates with other measurements in the literature, we found 53 ± 18% of the present stellar mass of early-type galaxies was assembled at z = 0.7.