  We present comprehensive characterization of the Galactic open cluster M 36.
Some two hundred member candidates, with an estimated contamination rate of
$\sim$8%, have been identified on the basis of proper motion and parallax
measured by the $Gaia$ DR2. The cluster has a proper motion grouping around
($\mu_{\alpha} \cos\delta = -$0.15 $\pm$ 0.01 mas yr$^{-1}$, and $\mu_{\delta}
= -$3.35 $\pm$ 0.02 mas yr$^{-1}$), distinctly separated from the field
population. Most member candidates have parallax values 0.7$-$0.9 mas, with a
median value of 0.82 $\pm$ 0.07 mas (distance $\sim$1.20 $\pm$ 0.13 kpc). The
angular diameter of 27$'$ $\pm$ $0\farcm4$ determined from the radial density
profile then corresponds to a linear extent of 9.42 $\pm$ 0.14 pc. With an
estimated age of $\sim$15 Myr, M 36 is free of nebulosity. To the south-west of
the cluster, we discover a highly obscured ($A_{V}$ up to $\sim$23 mag),
compact ($\sim$ $1\farcm9 \times 1\farcm2$) dense cloud, within which three
young stellar objects in their infancy (ages $\lesssim$ 0.2 Myr) are
identified. The molecular gas, 3.6 pc in extent, contains a total mass of
(2$-$3)$\times$10$^{2}$ M$_{\odot}$, and has a uniform velocity continuity
across the cloud, with a velocity range of $-$20 to $-$22 km s$^{-1}$,
consistent with the radial velocities of known star members. In addition, the
cloud has a derived kinematic distance marginally in agreement with that of the
star cluster. If physical association between M 36 and the young stellar
population can be unambiguously established, this manifests a convincing
example of prolonged star formation activity spanning up to tens of Myrs in
molecular clouds.
