  We investigate the stellar kinematics of the Galactic disc in 7 $<$ $R$ $<$
13\,kpc using a sample of 118\,945 red giant branch (RGB) stars from LAMOST and
Gaia. We characterize the median, dispersion and skewness of the distributions
of the 3D stellar velocities, actions and orbital parameters across the
age-metallicity and the disc $R$ -- $Z$ plane. Our results reveal abundant but
clear stellar kinematic patterns and structures in the age -- metallicity and
the disc $R$ -- $Z$ plane. The most prominent feature is the strong variations
of the velocity, action, and orbital parameter distributions from the young,
metal-rich thin disc to the old, metal-poor thick disc, a number of
smaller-scale structures -- such as velocity streams, north-south asymmetries,
and kinematic features of spiral arms -- are clearly revealed. Particularly,
the skewness of $V_{\phi}$ and $J_{\phi}$ reveals a new substructure at
$R\simeq12$\,kpc and $Z\simeq0$\,kpc, possibly related to dynamical effects of
spiral arms in the outer disc. We further study the stellar migration through
analysing the stellar orbital parameters and stellar birth radii. The results
suggest that the thick disc stars near the solar radii and beyond are mostly
migrated from the inner disc of $R\sim4 - 6$\,kpc due to their highly
eccentrical orbits. Stellar migration due to dynamical processes with angular
momentum transfer (churning) are prominent for both the old, metal-rich stars
(outward migrators) and the young metal-poor stars (inward migrators). The
spatial distribution in the $R$ -- $Z$ plane for the inward migrators born at a
Galactocentric radius of $>$12\,kpc show clear age stratifications, possibly an
evidence that these inward migrators are consequences of splashes triggered by
merger events of satellite galaxies that have been lasted in the past few giga
years.
