  We present the results obtained from the analysis of three XMM-Newton
observations of M83. The aims of the paper are studying the X-ray source
populations in M83 and calculating the X-ray luminosity functions of X-ray
binaries for different regions of the galaxy. We detected 189 sources in the
XMM-Newton field of view in the energy range of 0.2-12 keV. We constrained
their nature by means of spectral analysis, hardness ratios, studies of the
X-ray variability, and cross-correlations with catalogues in X-ray, optical,
infrared, and radio wavelengths. We identified and classified 12 background
objects, five foreground stars, two X-ray binaries, one supernova remnant
candidate, one super-soft source candidate and one ultra-luminous X-ray source.
Among these sources, we classified for the first time three active galactic
nuclei (AGN) candidates. We derived X-ray luminosity functions of the X-ray
sources in M83 in the 2-10 keV energy range, within and outside the D_25
ellipse, correcting the total X-ray luminosity function for incompleteness and
subtracting the AGN contribution. The X-ray luminosity function inside the D_25
ellipse is consistent with that previously observed by Chandra. The
Kolmogorov-Smirnov test shows that the X-ray luminosity function of the outer
disc and the AGN luminosity distribution are uncorrelated with a probability of
about 99.3%. We also found that the X-ray sources detected outside the D_25
ellipse and the uniform spatial distribution of AGNs are spatially uncorrelated
with a significance of 99.5%. We interpret these results as an indication that
part of the observed X-ray sources are X-ray binaries in the outer disc of M83.
