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 $Rsimeq12$,kpc and $Zsimeq0$,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 $Rsim4 - 6$,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.
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