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Full list of authors: Gilmore, G.; Randich, S.; Worley, C. C.; Hourihane, A.; Gonneau, A.; Sacco, G. G.; Lewis, J. R.; Magrini, L.; Francois, P.; Jeffries, R. D.; Koposov, S. E.; Bragaglia, A.; Alfaro, E. J.; Allende Prieto, C.; Blomme, R.; Korn, A. J.; Lanzafame, A. C.; Pancino, E.; Recio-Blanco, A.; Smiljanic, R.; Van Eck, S.; Zwitter, T.; Bensby, T.; Flaccomio, E.; Irwin, M. J.; Franciosini, E.; Morbidelli, L.; Damiani, F.; Bonito, R.; Friel, E. D.; Vink, J. S.; Prisinzano, L.; Abbas, U.; Hatzidimitriou, D.; Held, E., V; Jordi, C.; Paunzen, E.; Spagna, A.; Jackson, R. J.; Maiz Apellaniz, J.; Asplund, M.; Bonifacio, P.; Feltzing, S.; Binney, J.; Drew, J.; Ferguson, A. M. N.; Micela, G.; Negueruela, I; Prusti, T.; Rix, H-W; Vallenari, A.; Bergemann, M.; Casey, A. R.; de Laverny, P.; Frasca, A.; Hill, V; Lind, K.; Sbordone, L.; Sousa, S. G.; Adibekyan, V; Caffau, E.; Daflon, S.; Feuillet, D. K.; Gebran, M.; Gonzalez Hernandez, J., I; Guiglion, G.; Herrero, A.; Lobel, A.; Montes, D.; Morel, T.; Ruchti, G.; Soubiran, C.; Tabernero, H. M.; Tautvaisiene, G.; Traven, G.; Valentini, M.; Van der Swaelmen, M.; Villanova, S.; Vazquez, C. Viscasillas; Bayo, A.; Biazzo, K.; Carraro, G.; Edvardsson, B.; Heiter, U.; Jofre, P.; Marconi, G.; Martayan, C.; Masseron, T.; Monaco, L.; Walton, N. A.; Zaggia, S.; Borsen-Koch, V. Aguirre; Alves, J.; Balaguer-Nunez, L.; Barklem, P. S.; Barrado, D.; Bellazzini, M.; Berlanas, S. R.; Binks, A. S.; Bressan, A.; Capuzzo-Dolcetta, R.; Casagrande, L.; Casamiquela, L.; Collins, R. S.; D'Orazi, V; Dantas, M. L. L.; Debattista, V. P.; Delgado-Mena, E.; Di Marcantonio, P.; Drazdauskas, A.; Evans, N. W.; Famaey, B.; Franchini, M.; Fremat, Y.; Fu, X.; Geisler, D.; Gerhard, O.; Solares, E. A. Gonzalez; Grebel, E. K.; Gutierrez Albarran, M. L.; Jimenez-Esteban, F.; Jonsson, H.; Khachaturyants, T.; Kordopatis, G.; Kos, J.; Lagarde, N.; Ludwig, H-G; Mahy, L.; Mapelli, M.; Marfil, E.; Martell, S. L.; Messina, S.; Miglio, A.; Minchev, I; Moitinho, A.; Montalban, J.; Monteiro, M. J. P. F. G.; Morossi, C.; Mowlavi, N.; Mucciarelli, A.; Murphy, D. N. A.; Nardetto, N.; Ortolani, S.; Paletou, F.; Palous, J.; Pickering, J. C.; Quirrenbach, A.; Fiorentin, P. Re; Read, J., I; Romano, D.; Ryde, N.; Sanna, N.; Santos, W.; Seabroke, G. M.; Spina, L.; Steinmetz, M.; Stonkute, E.; Sutorius, E.; Thevenin, F.; Tosi, M.; Tsantaki, M.; Wright, N.; Wyse, R. F. G.; Zoccali, M.; Zorec, J.; Zucker, D. B.-- This is an Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited., Context. The Gaia-ESO Public Spectroscopic Survey is an ambitious project designed to obtain astrophysical parameters and elemental abundances for 100 000 stars, including large representative samples of the stellar populations in the Galaxy, and a well-defined sample of 60 (plus 20 archive) open clusters. We provide internally consistent results calibrated on benchmark stars and star clusters, extending across a very wide range of abundances and ages. This provides a legacy data set of intrinsic value, and equally a large wide-ranging dataset that is of value for the homogenisation of other and future stellar surveys and Gaia's astrophysical parameters. Aims. This article provides an overview of the survey methodology, the scientific aims, and the implementation, including a description of the data processing for the GIRAFFE spectra. A companion paper introduces the survey results. Methods. Gaia-ESO aspires to quantify both random and systematic contributions to measurement uncertainties. Thus, all available spectroscopic analysis techniques are utilised, each spectrum being analysed by up to several different analysis pipelines, with considerable effort being made to homogenise and calibrate the resulting parameters. We describe here the sequence of activities up to delivery of processed data products to the ESO Science Archive Facility for open use. Results. The Gaia-ESO Survey obtained 202 000 spectra of 115 000 stars using 340 allocated VLT nights between December 2011 and January 2018 from GIRAFFE and UVES. © G. Gilmore et al. 2022. Conclusions. The full consistently reduced final data set of spectra was released through the ESO Science Archive Facility in late 2020, with the full astrophysical parameters sets following in 2022. A companion article reviews the survey implementation, scientific highlights, the open cluster survey, and data products., Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.B-3002. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF/Osservatorio Astrofisico di Arcetri. Public access to the data products is via the ESO SAF, and the Gaia-ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council. This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell’ Istruzione, dell’ Università’ e della Ricerca (MIUR) in the form of the grant “Premiale VLT 2012”. The project presented here benefited in development from discussions held during the Gaia-ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. R.S. acknowledges support from the National Science Centre, Poland (2014/15/B/ST9/03981). This work was partly supported by the INAF grant for mainstream projects: “Enhancing the legacy of the Gaia-ESO Survey for open cluster science”. F.J.E. acknowledges financial support from the Spanish MINECO/FEDER through the grant AYA2017-84089 and MDM-2017-0737 at Centro de Astrobiología (CSIC-INTA), Unidad de Excelencia María de Maeztu, and from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement no. 824064 through the ESCAPE – the European Science Cluster of Astronomy and Particle Physics ESFRI Research Infrastructures project. T.B. was funded by the “The New Milky Way” project grant from the Knut and Alice Wallenberg Foundation. S.R.B. acknowledges support by the Spanish Government under grants AYA2015-68012-C2-2-P and PGC2018-093741-B-C21/C22 (MICIU/AEI/FEDER, UE). W.J.S. acknowledges CAPES for a PhD studentship. J.M.A. acknowledges support from the Spanish Government Ministerio de Ciencia e Innovación through grants AYA2013-40611-P, AYA2016-75931-C2-2-P, and PGC2018-095049-B-C22. T.M. and others from STAR institute, Liege, Belgium are grateful to Belgian F.R.S.-FNRS for support, and are also indebted for an ESA/PRODEX Belspo contract related to the Gaia Data Processing and Analysis Consortium and for support through an ARC grant for Concerted Research Actions financed by the Federation Wallonie-Brussels.. This research has been partially supported by the following grants: MIUR Premiale “Gaia-ESO survey” (PI S. Randich), MIUR Premiale “MiTiC: Mining the Cosmos” (PI B. Garilli), the ASI-INAF contract 2014-049-R.O: “Realizzazione attività tecniche/scientifiche presso ASDC” (PI Angelo Antonelli), Fondazione Cassa di Risparmio di Firenze, progetto: “Know the star, know the planet” (PI E. Pancino), and Progetto Main Stream INAF: “Chemo-dynamics of globular clusters: the Gaia revolution” (PI E. Pancino). V.A. acknowledges the support from Fundação para a Ciência e Tecnologia (FCT) through Investigador FCT contract nr. IF/00650/2015/CP1273/CT0001. A.J.K. acknowledges support by the Swedish National Space Agency (SNSA). A.B. acknowledges support by ANID, – Millennium Science Initiative Program – NCN19_171, and FONDECYT regular 1190748. E.M. acknowledges financial support from the Spanish State Research Agency (AEI) through project MDM-2017-0737 Unidad de Excelencia “María de Maeztu” – Centro de Astrobiología (CSIC-INTA). T.Z. acknowledges financial support of the Slovenian Research Agency (research core funding no. P1-0188) and the European Space Agency (Prodex Experiment Arrangement No. C4000127986). P.J. acknowledges support FONDECYT Regular 1200703. The work of I.N. is partially supported by the Spanish Government Ministerio de Ciencia, Innovación y Universidades under grant PGC2018-093741-B-C21 (MICIU/AEI/FEDER, UE). Funding for this work has been provided by the ARC Future Fellowship FT160100402. C.A.P. acknowledges financial support from the Spanish Government through research grants MINECO AYA 2014-56359-P, MINECO AYA2017-86389-P, and MICINN PID2020-117493GB-I00. S.F. was supported by the grants 2011-5042 and 2016-03412 from the Swedish Research Council and the project grant “The New Milky Way” from the Knut and Alice Wallenberg Foundation. C.A.S.U. is supported through STFC grants: ST/H004157/1, ST/J00541X/1, ST/M007626/1, ST/N005805/1, ST/T003081/1. Work reported here benefited from support through the GREAT-ITN FP7 project Grant agreement ID: 264895. D.K.F. acknowledges funds from the Alexander von Humboldt Foundation in the framework of the Sofja Kovalevskaja Award endowed by the Federal Ministry of Education and Research and the grant 2016-03412 from the Swedish Research Council. A.H. acknowledges support from the Spanish Government Ministerio de Ciencia e Innovación and ERD Funds through grants PGC-2018-091 3741-B-C22 and CEX2019-000920-S. X.F. acknowledges the support of China Postdoctoral Science Foundation 2020M670023. M.L.L.D. acknowledges the Polish NCN grant number 2019/34/E/ST9/00133. Part of this work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 138713538 – SFB 881 (“The Milky Way System”, subproject A09). M.Z. acknowledges support from the National Agency for Research and Development (ANID) grants: FONDECYT Regular 1191505, Millennium Institute of Astrophysics ICN12-009, BASAL Center for Astrophysics and Associated Technologies AFB-170002. R.B. acknowledges support from the project PRIN-INAF 2019 “Spectroscopically Tracing the Disk Dispersal Evolution”. H.M.T. acknowledges financial support from the Agencia Estatal de Investigación of the Ministerio de Ciencia, Innovación y Universidades through projects PID2019-109522GB-C51,54/AEI/10.13039/501100011033, and the Centre of Excellence “María de Maeztu” award to Centro de Astrobiología (MDM-2017-0737). J.I.G.H. acknowledges financial support from the Spanish Ministry of Science and Innovation (MICINN) project AYA2017-86389-P, and also from the Spanish MICINN under 2013 Ramѳn y Cajal program RYC-2013-14875. V.P.D. is supported by STFC Consolidated grant ST/R000786/1. N.L. acknowledges financial support from “Programme National de Physique Stellaire” (PNPS) and the “Programme National Cosmology et Galaxies (PNCG)” of CNRS/INSU, France. A.R.C. is supported in part by the Australian Research Council through a Discovery Early Career Researcher Award (DE190100656). Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. P.S.B. is supported by the Swedish Research Council through individual project grants with contract Nos. 2016-03765 and 2020-03404. A.M. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 772293 – project ASTEROCHRONOMETRY). J.P. was supported by the project RVO: 67985815. E.D.M. acknowledges the support from FCT through the research grants UIDB/04434/2020 & UIDP/04434/2020 and through Investigador FCT contract IF/00849/2015/CP1273/CT0003. This work was (partially) supported by the Spanish Ministry of Science, Innovation and University (MICIU/FEDER, UE) through grant RTI2018-095076-B-C21, and the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia 'María de Maeztu’) through grant CEX2019-000918-M. S.L.M. acknowledges the support of the UNSW Scientia Fellowship program and the Australian Research Council through Discovery Project grant DP180101791. GT acknowledges financial support of the Slovenian Research Agency (research core funding No. P1-0188) and the European Space Agency (Prodex Experiment Arrangement No. C4000127986). S.G.S acknowledges the support from FCT through Investigador FCT contract nr. CEECIND/00826/2018 and POPH/FSE (EC). H.G.L. acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 138713538 – SFB 881 (“The Milky Way System”, subproject A04). This work was (partially) supported by the Spanish Ministry of Science, Innovation and University (MICIU/FEDER, UE) through grant RTI2018-095076-B-C21, and the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia ’María de Maeztu’) through grant CEX2019-000918-M. T.K. is supported by STFC Consolidated grant ST/R000786/1. M.V. acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, project number: 428473034). T.M. is supported by a grant from the Fondation ULB. We acknowledge financial support from the Universidad Complutense de Madrid (UCM) and by the Spanish Ministerio de Ciencia, Innovación y Universidades, Ministerio de Economía y Competitividad, from project AYA2016-79425-C3-1-P and PID2019-109522GB-C5[4]/AEI/10.13039/501100011033. U.H. acknowledges support from the Swedish National Space Agency (SNSA/Rymdstyrelsen). D.G. gratefully acknowledges support from the Chilean Centro de Excelencia en Astrofísica y Tecnologías Afines (CATA) BASAL grant AFB-170002. D.G. also acknowledges financial support from the Dirección de Investigación y Desarrollo de la Universidad de La Serena through the Programa de Incentivo a la Investigación de Académicos (PIA-DIDULS). A. Lobel acknowledges support in part by the Belgian Federal Science Policy Office under contract No. BR/143/A2/BRASS. We acknowledge financial support from the Universidad Complutense de Madrid (UCM) and by the Spanish Ministerio de Ciencia, Innovación y Universidades, Ministerio de Economía y Competitividad, from project AYA2016-79425-C3-1-P and PID2019-109522GB-C5[4]/AEI/10.13039/501100011033. A.M. acknowledges the support from the Portuguese Fundação para a Ciência e a Tecnologia (FCT) through the Portuguese Strategic Programme UID/FIS/00099/2019 for CENTRA. T.M. acknowledges financial support from the Spanish Ministry of Science and Innovation (MICINN) through the Spanish State Research Agency, under the Severo Ochoa Program 2020-2023 (CEX2019-000920-S). E.J.A. acknowledges funding from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de An- dalucía (SEV-2017-0709).