  We present DESI observations of the inner halo of M31, which reveal the
kinematics of a recent merger - a galactic immigration event - in exquisite
detail. Of the 11,416 sources studied in 3.75 hour of on-sky exposure time,
7,438 are M31 sources with well measured radial velocities. The observations
reveal intricate coherent kinematic structure in the positions and velocities
of individual stars: streams, wedges, and chevrons. While hints of coherent
structures have been previously detected in M31, this is the first time they
have been seen with such detail and clarity in a galaxy beyond the Milky Way.
We find clear kinematic evidence for shell structures in the Giant Stellar
Stream, the Northeast Shelf and Western Shelf regions. The kinematics are
remarkably similar to the predictions of dynamical models constructed to
explain the spatial morphology of the inner halo. The results are consistent
with the interpretation that much of the substructure in the inner halo of M31
is produced by a single galactic immigration event 1 - 2 Gyr ago. Significant
numbers of metal-rich stars ([Fe/H]$>-0.5$) are present in all of the detected
substructures, suggesting that the immigrating galaxy had an extended star
formation history. We also investigate the ability of the shells and Giant
Stellar Stream to constrain the gravitational potential of M31, and estimate
the mass within a projected radius of 125 kpc to be ${\rm log_{10}}\, M_{\rm
NFW}(<125\,{\rm kpc})/M_\odot = 11.80_{-0.10}^{+0.12}$. The results herald a
new era in our ability to study stars on a galactic scale and the immigration
histories of galaxies.
