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We have obtained a series of deep X-ray images of the nearby galaxy M83 using Chandra, with a total exposure of 729 ks. Combining the new data with earlier archival observations totaling 61 ks, we find 378 point sources within the D25 contour of the galaxy. We find 80 more sources, mostly background active galactic nuclei (AGNs), outside of the D25 contour. Of the X-ray sources, 47 have been detected in a new radio survey of M83 obtained using the Australia Telescope Compact Array. Of the X-ray sources, at least 87 seem likely to be supernova remnants (SNRs), based on a combination of their properties in X-rays and at other wavelengths. We attempt to classify the point source population of M83 through a combination of spectral and temporal analysis. As part of this effort, we carry out an initial spectral analysis of the 29 brightest X-ray sources. The soft X-ray sources in the disk, many of which are SNRs, are associated with the spiral arms, while the harder X-ray sources, mostly X-ray binaries (XRBs), do not appear to be. After eliminating AGNs, foreground stars, and identified SNRs from the sample, we construct the cumulative luminosity function (CLF) of XRBs brighter than 8 × 1035 erg s–1. Despite M83's relatively high star formation rate, the CLF indicates that most of the XRBs in the disk are low mass XRBs.