We present deep, photometrically calibrated BVRJHK images of the nearby interacting galaxy pair NGC 4038/39 (``The Antennae). Color maps of the images are derived, and those using the B, V, and K-bands are analyzed with techniques developed for examining the colors of stars. From these data we derive pixel-by-pixel maps of the distributions of stellar populations and dust extinction for the galaxies. Analysis of the stellar population map reveals two distinct episodes of recent star formation: one currently in progress and a second that occurred ~600 Myr ago. A roughly 15 Gyr-old population is found which traces the old disks of the galaxies and the bulge of NGC 4038. The models used successfully reproduce the locations of clusters, and the ages we derive are consistent with those found from previous Hubble Space Telescope observations of individual star clusters. We also find 5 luminous ``super star clusters in our K-band images that do not appear in the B or V-band images. These clusters are located in the overlap region between the two galaxies, and are hidden by dust with visual extinctions of A_V ~> 3 mag. The techniques we describe in this paper should be generally applicable to the study of stellar populations in galaxies for which detailed spatial resolution with Hubble is not possible.
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