  We present an analysis of the proper motion of the Andromeda galaxy (M31),
based on the Early Third Data Release of the {\it Gaia} mission. We use the
{\it Gaia} photometry to select young blue main sequence stars, and apply
several quality cuts to obtain clean samples of these tracers. After correcting
the proper motion measurements for the internal rotation of the M31 disk
motion, we derive an apparent motion of $53.6 \pm 7.7 \, \mu as/yr$ with
respect to the {\it Gaia} reference frame, or $62.0 \pm 9.6 \, \mu as/yr$ after
applying a zero-point correction determined from quasars within $20\deg$ from
M31. Accounting for the Solar reflex motion we deduce a relative velocity
between Andromeda and the Milky way (in a non-rotating frame at the current
location of the Sun) of $46.7 \pm 40.8 \, {\rm km.s^{-1}}$, (along right
ascension) and $-64.7 \pm 31.7 \, {\rm km.s^{-1}}$ (along declination), with a
total transverse velocity of $V_{\rm trans} = 79.8 \pm 38.3 \, {\rm
km.s^{-1}}$. These values are consistent with (but more accurate than) earlier
Hubble Space Telescope measurements that predict future merger between the two
galaxies. We also note a surprisingly large difference in the derived proper
motion between the blue stars in M31 and samples of red stars that appear to
lie in that galaxy. We suspect that this is due to contamination from a
foreground stellar stream.
