  The FIRBACK (Far Infrared BACKground) survey is one of the deepest imaging
surveys carried out at 170 microns with ISOPHOT onboard ISO, and is aimed at
the study of the structure of the Cosmic Far Infrared Background. This paper
provides the analysis of resolved sources. After a validated process of data
reduction and calibration, we perform intensive simulations to optimize the
source extraction, measure the confusion noise (sigma_c = 45 mJy), and give the
photometric and astrometric accuracies. 196 galaxies with flux S > 3 sigma_c
are detected in the area of 3.89 square degrees. Counts of sources with flux S
> 4 sigma_c present a steep slope of 3.3 +/- 0.6 on a differential "logN-logS"
plot between 180 and 500 mJy. As a consequence, the confusion level is high and
will impact dramatically on future IR deep surveys. This strong evolution,
compared with a slope of 2.5 from Euclidian geometry, is in line with models
implying a strongly evolving Luminous Infrared Galaxy population. The resolved
sources account for less than 10% of the Cosmic Infrared Background at 170
microns, which is expected to be resolved into sources in the 1 to 10 mJy
range.
