  We present the data analysis and the X-ray source counts for the first season
of XMM-Newton observations in the COSMOS field. The survey covers ~2 deg^2
within the region of sky bounded by 9^h57.5^m<R.A.<10^h03.5^m;
1^d27.5^m<DEC<2^d57.5^m with a total net integration time of 504 ks. A maximum
likelihood source detection was performed in the 0.5-2 keV, 2-4.5 keV and
4.5-10 keV energy bands and 1390 point-like sources were detected in at least
one band. Detailed Monte Carlo simulations were performed to fully test the
source detection method and to derive the sky coverage to be used in the
computation of the logN-logS relations. The 0.5--2 keV and 2--10 keV
differential logN-logS were fitted with a broken power-law model which revealed
a Euclidean slope (alpha~2.5) at the bright end and a flatter slope (alpha~1.5)
at faint fluxes. In the 5--10 keV energy band a single power-law provides an
acceptable fit to the observed source counts with a slope alpha~2.4. A
comparison with the results of previous surveys shows good agreement in all the
energy bands under investigation in the overlapping flux range.
  We also notice a remarkable agreement between our logN-logS relations and the
most recent model of the XRB. The slightly different normalizations observed in
the source counts of COSMOS and previous surveys can be largely explained as a
combination of low counting statistics and cosmic variance introduced by the
large scale structure.

Astrophysics