  This paper describes the mapmaking procedure applied to Planck LFI (Low
Frequency Instrument) data. The mapmaking step takes as input the calibrated
timelines and pointing information. The main products are sky maps of $I,Q$,
and $U$ Stokes components. For the first time, we present polarization maps at
LFI frequencies. The mapmaking algorithm is based on a destriping technique,
enhanced with a noise prior. The Galactic region is masked to reduce errors
arising from bandpass mismatch and high signal gradients. We apply horn-uniform
radiometer weights to reduce effects of beam shape mismatch. The algorithm is
the same as used for the 2013 release, apart from small changes in parameter
settings. We validate the procedure through simulations. Special emphasis is
put on the control of systematics, which is particularly important for accurate
polarization analysis. We also produce low-resolution versions of the maps, and
corresponding noise covariance matrices. These serve as input in later analysis
steps and parameter estimation. The noise covariance matrices are validated
through noise Monte Carlo simulations. The residual noise in the map products
is characterized through analysis of half-ring maps, noise covariance matrices,
and simulations.
