The quest for the cosmological parameters that describe our universe continues to motivate the scientific community to undertake very large survey initiatives across the electromagnetic spectrum. Over the past two decades, the Chandra and XMM-Newton observatories have sup- ported numerous studies of X-ray-selected clusters of galaxies, active galactic nuclei (AGNs), and the X-ray background. The present paper is the first in a series reporting results of the XXL-XMM survey; it comes at a time when the Planck mission results are being finalised. We present the XXL Survey, the largest XMM programme totaling some 6.9Ms to date and involving an international consortium of roughly 100 members. The XXL Survey covers two extragalactic areas of 25deg^2^ each at a point-source sensitivity of ~5x10^-15^erg/s/cm^2^ in the [0.5-2]keV band (completeness limit). The survey's main goals are to provide constraints on the dark energy equation of state from the space-time distribution of clusters of galaxies and to serve as a pathfinder for future, wide-area X-ray missions. We review science objectives, including cluster studies, AGN evolution, and large-scale structure, that are being conducted with the support of approximately 30 follow-up programmes. List of XXL papers: I. Scientific motivations - XMM-Newton observing plan - Follow-up observations and simulation programme. II. The bright cluster sample: catalogue and luminosity function. III. Luminosity-temperature relation of the bright cluster sample. IV. Mass-temperature relation of the bright cluster sample. VI. The 1000 brightest X-ray point sources. VII. A supercluster of galaxies at z = 0.43. VIII. MUSE characterisation of intracluster light in a z~0.53 cluster of galaxies. IX. Optical overdensity and radio continuum analysis of a supercluster at z=0.43. X. K-band luminosity - weak-lensing mass relation for groups and clusters of galaxies. XI. ATCA 2.1 GHz continuum observations. XII. Optical spectroscopy of X-ray-selected clusters and the frequency of AGN in superclusters. XIII. Baryon content of the bright cluster sample. XIV. AAOmega redshifts for the southern XXL field.