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The authors wish to thank J.M. Torrejón for the organization of the Athena-multi-messenger Workshops, held on November 27 - 29, 2018, in Alicante, Spain and on 5 May 2020 - 6 May 2020 in videoconference., In this paper we explore the scientific synergies between Athena and some of the key multi-messenger facilities that should be operative concurrently with Athena. These facilities include LIGO A+, Advanced Virgo+ and future detectors for ground-based observation of gravitational waves (GW), LISA for space-based observations of GW, IceCube and KM3NeT for neutrino observations, and CTA for very high energy observations. These science themes encompass pressing issues in astrophysics, cosmology and fundamental physics such as: the central engine and jet physics in compact binary mergers, accretion processes and jet physics in Super-Massive Binary Black Holes (SMBBHs) and in compact stellar binaries, the equation of state of neutron stars, cosmic accelerators and the origin of Cosmic Rays (CRs), the origin of intermediate and high-Z elements in the Universe, the Cosmic distance scale and tests of General Relativity and the Standard Model. Observational strategies for implementing the identified science topics are also discussed. A significant part of the sources targeted by multi-messenger facilities is of transient nature. We have thus also discussed the synergy of Athena with wide-field high-energy facilities, taking THESEUS as a case study for transient discovery. This discussion covers all the Athena science goals that rely on follow-up observations of high-energy transients identified by external observatories, and includes also topics that are not based on multi-messenger observations, such as the search for missing baryons or the observation of early star populations and metal enrichment at the cosmic dawn with Gamma-Ray Bursts (GRBs)., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature., This research has been supported by the European Union’s Horizon 2020 programme under the AHEAD (grant agreement number 654215) and AHEAD2020 project (grant agreement n. 871158). FJC and SMN acknowledges funding under project RTI2018-096686-B-C21 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, and by the Unidad de Excelencia María de Maeztu, ref. MDM-2017-0765.