  The European Space Agency's Planck satellite, which was dedicated to studying
the early Universe and its subsequent evolution, was launched on 14 May 2009.
It scanned the microwave and submillimetre sky continuously between 12 August
2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine
frequency bands from 30 to 857GHz. This paper presents the cosmological legacy
of Planck, which currently provides our strongest constraints on the parameters
of the standard cosmological model and some of the tightest limits available on
deviations from that model. The 6-parameter LCDM model continues to provide an
excellent fit to the cosmic microwave background data at high and low redshift,
describing the cosmological information in over a billion map pixels with just
six parameters. With 18 peaks in the temperature and polarization angular power
spectra constrained well, Planck measures five of the six parameters to better
than 1% (simultaneously), with the best-determined parameter (theta_*) now
known to 0.03%. We describe the multi-component sky as seen by Planck, the
success of the LCDM model, and the connection to lower-redshift probes of
structure formation. We also give a comprehensive summary of the major changes
introduced in this 2018 release. The Planck data, alone and in combination with
other probes, provide stringent constraints on our models of the early Universe
and the large-scale structure within which all astrophysical objects form and
evolve. We discuss some lessons learned from the Planck mission, and highlight
areas ripe for further experimental advances.
