  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 homogenisation of other and future stellar surveys
and Gaia's astrophysical parameters. 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
(arXiv:2206.02901) introduces the survey results. 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. 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. 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.
