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We describe the POLAMI program for the monitoring of all four Stokesparameters of a sample of bright radio-loud active galactic nuclei with theIRAM 30m telescope at 3.5 and 1.3mm. The program started in October 2006 andaccumulated, until August 2014, 2300 observations at 3.5mm, achieving a mediantime sampling interval of 22 days for the sample of 37 sources. This firstpaper explains the source selection, mostly blazars, the observing strategy anddata calibration, and gives the details of the instrumental polarisationcorrections. The sensitivity (1sigma) reached at 3.5mm is 0.5% (linearpolarisation degree), 4.7 deg. (polarisation angle), and 0.23% (circularpolarisation), while the corresponding values at 1.3mm are 1.7%, 9.9 deg., and0.72%, respectively. The data quality is demonstrated by the time sequences ofour calibrators Mars and Uranus. For the quasar 3C286, widely used as a linearpolarisation calibrator, we give improved estimates of its linear polarisation,and show for the first time occasional detections of its weak circularpolarisation, which suggests a small level of variability of the source atmillimeter wavelengths.

POLAMI: Polarimetric Monitoring of Active Galactic Nuclei at Millimetre Wavelengths. I. The program, calibration, and calibrators data products