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Full list of authors: Dey, Arjun; Najita, Joan R.; Koposov, Sergey E.; Josephy-Zack, J.; Maxemin, Gabriel; Bell, Eric F.; Poppett, C.; Patel, E.; Beraldo e Silva, L.; Raichoor, A.; Schlegel, D.; Lang, D.; Meisner, A.; Myers, Adam D.; Aguilar, J.; Ahlen, S.; Allende Prieto, C.; Brooks, D.; Cooper, A. P.; Dawson, K. S.; de la Macorra, A.; Doel, P.; Font-Ribera, A.; Garcia-Bellido, Juan; Gontcho, S. Gontcho A.; Guy, J.; Honscheid, K.; Kehoe, R.; Kisner, T.; Kremin, A.; Landriau, M.; Le Guillou, L.; Levi, Michael E.; Li, T. S.; Martini, Paul; Miquel, R.; Moustakas, J.; Nie, Jundan; Palanque-Delabrouille, N.; Prada, F.; Schlafly, E. F.; Sharples, Ray M.; Tarle, Gregory; Ting, Yuan-Sen; Tyas, L.; Valluri, M.; Wechsler, Risa H.; Zou, H.--This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited., We present Dark Energy Spectroscopic Instrument (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 hr of on-sky exposure time, 7438 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 ${\mathrm{log}}_{10}\,{M}_{\mathrm{NFW}}(\lt 125\,\mathrm{kpc})/{M}_{\odot }={11.80}_{-0.10}^{+0.12}$. The results herald a new era in our ability to study stars on a galactic scale and the immigration histories of galaxies. © 2023. The Author(s). Published by the American Astronomical Society., A.D. and J.N.'s research activities are supported by the NSF's NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. A.D. and J.N.'s research is also supported in part by Fellowships from the John Simon Guggenheim Memorial Foundation and by the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics. J.N. also acknowledges support from the Harvard Radcliffe Fellowship Program of the Radcliffe Institute for Advanced Study at Harvard University. J.N., G.M., and J.J.-Z. acknowledge support from the Harvard University's Radcliffe Research Partners Program of the Radcliffe Institute for Advanced Study. E.F.B. is grateful for support from the National Science Foundation through grant NSF-AST 2007065. L.B.S. acknowledges NASA-ATP award 80NSSC20K0509 and Science Foundation AAG grant AST-2009122. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under contract No. DE-AC02-05CH11231, and by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract; additional support for DESI is provided by the U.S. National Science Foundation, Division of Astronomical Sciences under contract No. AST-0950945 to the NSF's National Optical-Infrared Astronomy Research Laboratory; the Science and Technologies Facilities Council of the United Kingdom; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; the French Alternative Energies and Atomic Energy Commission (CEA); the National Council of Science and Technology of Mexico (CONACYT); the Ministry of Science and Innovation of Spain (MICINN), and by the DESI Member Institutions: https://www.desi.lbl.gov/collaborating-institutions. The authors are honored to be permitted to conduct scientific research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. This work was partially supported by a grant from the Simons Foundation., With funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2021-001131-S).