  We present an overview of the sample of northern hemisphere white dwarfs
within 40 pc of the Sun detected from $Gaia$ Data Release 2 (DR2). We find that
521 sources are spectroscopically confirmed degenerate stars, 111 of which were
first identified as white dwarf candidates from $Gaia$ DR2 and followed-up
recently with the William Herschel Telescope and Gran Telescopio Canarias.
Three additional white dwarf candidates remain spectroscopically unobserved and
six unresolved binaries are known to include a white dwarf but were not in our
initial selection of white dwarfs in the $Gaia$ DR2 Hertzsprung-Russell diagram
(HRD). Atmospheric parameters are calculated from $Gaia$ and Pan-STARRS
photometry for all objects in the sample, confirming most of the trends
previously observed in the much smaller 20 pc sample. Local white dwarfs are
overwhelmingly consistent with Galactic disc kinematics, with only four halo
candidates. We find that DAZ white dwarfs are significantly less massive than
the overall DA population ($\overline{M}_\mathrm{DAZ} =
0.59\,\mathrm{M}_\odot$, $\overline{M}_\mathrm{DA} = 0.66\,\mathrm{M}_\odot$).
It may suggest that planet formation is less efficient at higher mass stars,
producing more massive white dwarfs. We detect a sequence of crystallised white
dwarfs in the mass range from $0.6\ \lesssim M/\mathrm{M}_\odot \lesssim\
1.0\,$ and find that the vast majority of objects on the sequence have standard
kinematic properties that correspond to the average of the sample, suggesting
that their nature can be explained by crystallisation alone. We also detect 56
wide binaries including a white dwarf and 26 double degenerates.
