  CONTEXT. The Gaia Collaboration has used Gaia-DR2 sources with
six-dimensional (6D) phase space information to derive kinematical maps within
5 kpc of the Sun, which is a reachable range for stars with relative error in
distance lower than 20%.
  AIMS. Here we aim to extend the range of distances by a factor of two to
three, thus adding the range of Galactocentric distances between 13 kpc and 20
kpc to the previous maps, with their corresponding error and root mean square
values.
  METHODS. We make use of the whole sample of stars of Gaia-DR2 including
radial velocity measurements, which consists in more than seven million
sources, and we apply a statistical deconvolution of the parallax errors based
on the Lucy's inversion method of the Fredholm integral equations of the first
kind, without assuming any prior.
  RESULTS. The new extended maps provide lots of new and corroborated
information about the disk kinematics: significant departures of circularity in
the mean orbits with radial Galactocentric velocities between -20 and +20 km/s
and vertical velocities between -10 and +10 km/s; variations of the azimuthal
velocity with position; asymmetries between the northern and the southern
Galactic hemispheres, especially towards the anticenter that includes a larger
azimuthal velocity in the south; and others.
  CONCLUSIONS. These extended kinematical maps can be used to investigate the
different dynamical models of our Galaxy, and we will present our own analyses
in the forthcoming second part of this paper. At present, it is evident that
the Milky Way is far from a simple stationary configuration in rotational
equilibrium, but is characterized by streaming motions in all velocity
components with conspicuous velocity gradients.
