  We present the results of a deep X-ray survey conducted with XMM-Newton,
centred on the UK ROSAT 13H deep field area. This region covers 0.18 deg^2 and
is the first of two areas covered with XMM-Newton as part of an extensive
multi-wavelength survey designed to study the nature and evolution of the faint
X-ray source population. We have produced detailed Monte-Carlo simulations to
obtain a quantitative characterisation of the source detection procedure and to
assess the reliability of the resultant sourcelist. We use the simulations to
establish a likelihood threshold above which we expect less than 7 (3%) of our
sources to be spurious. We present the final catalogue of 225 sources. Within
the central 9 arcmin, 68 per cent of source positions are accurate to 2 arcsec,
making optical follow-up relatively straightforward. We construct the N(>S)
relation in four energy bands: 0.2-0.5 keV, 0.5-2 keV, 2-5 keV and 5-10 keV. In
all but our highest energy band we find that the source counts can be
represented by a double powerlaw with a bright end slope consistent with the
Euclidean case and a break around 10^-14 cgs. Below this flux the counts
exhibit a flattening. Our source counts reach densities of 700, 1300, 900 and
300 deg^-2 at fluxes of 4.1x10^-16, 4.5x10^-16, 1.1x10^-15 and 5.3x10^-15 cgs
in the 0.2-0.5, 0.5-2, 2-5 and 5-10 keV energy bands respectively. We have
compared our source counts with those in the two Chandra deep fields and
Lockman hole and find our source counts to be amongst the highest of these
fields in all energy bands. We resolve >51% (>50%) of the X-ray background
emission in the 1-2 keV (2-5 keV) energy bands.
