Abstract. The FIRBACK (Far Infrared BACKground) survey is one of the deepest imaging surveys carried out at 170 µm 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 (σc = 45 mJy), and give the photometric and astrometric accuracies. 196 galaxies with flux S > 3σc are detected in the area of 3.89 square degrees. Counts of sources with flux S > 4σc present a steep slope of 3.3 ± 0.6 on a differential "log N-log S" 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 µm, which is expected to be resolved into sources in the 1 to 10 mJy range.Key words. cosmology: miscellaneous -galaxies: infrared -galaxies: evolution -galaxies: statistics Send offprint requests to: H. Dole, e-mail: hdole@as.arizona.edu Based on observations with ISO, an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, The Netherlands and the UK) and with the participation of ISAS and NASA.Tables 7 to 13 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via

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