  We test the statistical isotropy and Gaussianity of the cosmic microwave
background (CMB) anisotropies using observations made by the Planck satellite.
Our results are based mainly on the full Planck mission for temperature, but
also include some polarization measurements.
  In particular, we consider the CMB anisotropy maps derived from the
multi-frequency Planck data by several component-separation methods. For the
temperature anisotropies, we find excellent agreement between results based on
these sky maps over both a very large fraction of the sky and a broad range of
angular scales, establishing that potential foreground residuals do not affect
our studies.
  Tests of skewness, kurtosis, multi-normality, N-point functions, and
Minkowski functionals indicate consistency with Gaussianity, while a power
deficit at large angular scales is manifested in several ways, for example low
map variance. The results of a peak statistics analysis are consistent with the
expectations of a Gaussian random field. The "Cold Spot" is detected with
several methods, including map kurtosis, peak statistics, and mean temperature
profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting
it with several independent tests, and address the subject of a posteriori
correction. Tests of directionality suggest the presence of angular clustering
from large to small scales, but at a significance that is dependent on the
details of the approach. We perform the first examination of polarization data,
finding the morphology of stacked peaks to be consistent with the expectations
of statistically isotropic simulations. Where they overlap, these results are
consistent with the Planck 2013 analysis based on the nominal mission data and
provide our most thorough view of the statistics of the CMB fluctuations to
date.
