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We present galaxy luminosity functions at 3.6, 4.5, 5.8, and 8.0 micronmeasured by combining photometry from the IRAC Shallow Survey with redshiftsfrom the AGN and Galaxy Evolution Survey of the NOAO Deep Wide-Field SurveyBootes field. The well-defined IRAC samples contain 3800-5800 galaxies for the3.6-8.0 micron bands with spectroscopic redshifts and z < 0.6. We obtainedrelatively complete luminosity functions in the local redshift bin of z < 0.2for all four IRAC channels that are well fit by Schechter functions. We foundsignificant evolution in the luminosity functions for all four IRAC channelsthat can be fit as an evolution in M* with redshift, \Delta M* = Qz. While wemeasured Q=1.2\pm0.4 and 1.1\pm0.4 in the 3.6 and 4.5 micron bands consistentwith the predictions from a passively evolving population, we obtainedQ=1.8\pm1.1 in the 8.0 micron band consistent with other evolving starformation rate estimates. We compared our LFs with the predictions ofsemi-analytical galaxy formation and found the best agreement at 3.6 and 4.5micron, rough agreement at 8.0 micron, and a large mismatch at 5.8 micron.These models also predicted a comparable Q value to our luminosity functions at8.0 micron, but predicted smaller values at 3.6 and 4.5 micron. We alsomeasured the luminosity functions separately for early and late-type galaxies.While the luminosity functions of late-type galaxies resemble those for thetotal population, the luminosity functions of early-type galaxies in the 3.6and 4.5 micron bands indicate deviations from the passive evolution model,especially from the measured flat luminosity density evolution. Combining ourestimates with other measurements in the literature, we found (53\pm18)% of thepresent stellar mass of early-type galaxies has been assembled at z=0.7.

Mid-Infrared Galaxy Luminosity Functions from the AGN and Galaxy Evolution Survey