  This paper describes the processing applied to the HFI cleaned time-ordered
data to produce photometrically calibrated maps. HFI observes the sky over a
broad range of frequencies, from 100 to 857 GHz. To get the best accuracy on
the calibration on such a large range, two different photometric calibration
schemes have to be used. The 545 and 857 \GHz\ data are calibrated using Uranus
and Neptune flux density measurements, compared with models of their
atmospheric emissions to calibrate the data. The lower frequencies (below 353
GHz) are calibrated using the cosmological microwave background dipole.One of
the components of this anisotropy results from the orbital motion of the
satellite in the Solar System, and is therefore time-variable. Photometric
calibration is thus tightly linked to mapmaking, which also addresses low
frequency noise removal. The 2013 released HFI data show some evidence for
apparent gain variations of the HFI bolometers' detection chain. These
variations were identified by comparing observations taken more than one year
apart in the same configuration. We developed an effective correction to limit
its effect on calibration, and assess its accuracy. We present several methods
used to estimate the precision of the photometric calibration. We distinguish
relative (from one detector to another, or from one frequency to another) and
absolute uncertainties. In both cases, we found that these uncertainties range
from a few $10^{-3}$ to several per cents from 100 to 857 GHz. We describe the
pipeline producing the maps from the HFI timelines, based on the photometric
calibration parameters and we detail the scheme used to a posteriori set the
zero level of the maps. We also briefly discuss the cross-calibration between
HFI and the SPIRE instrument on board Herschel. We finally summarize the basic
characteristics of the set of the HFI maps from the 2013 Planck data release.
