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We present an overview of the sample of northern hemisphere white dwarfswithin 40 pc of the Sun detected from $Gaia$ Data Release 2 (DR2). We find that521 sources are spectroscopically confirmed degenerate stars, 111 of which werefirst identified as white dwarf candidates from $Gaia$ DR2 and followed-uprecently with the William Herschel Telescope and Gran Telescopio Canarias.Three additional white dwarf candidates remain spectroscopically unobserved andsix unresolved binaries are known to include a white dwarf but were not in ourinitial selection of white dwarfs in the $Gaia$ DR2 Hertzsprung-Russell diagram(HRD). Atmospheric parameters are calculated from $Gaia$ and Pan-STARRSphotometry for all objects in the sample, confirming most of the trendspreviously observed in the much smaller 20 pc sample. Local white dwarfs areoverwhelmingly consistent with Galactic disc kinematics, with only four halocandidates. We find that DAZ white dwarfs are significantly less massive thanthe 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 whitedwarfs 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 standardkinematic properties that correspond to the average of the sample, suggestingthat their nature can be explained by crystallisation alone. We also detect 56wide binaries including a white dwarf and 26 double degenerates.

$Gaia$ white dwarfs within 40 pc II: the volume-limited northern hemisphere sample