Brussels insists it will only start discussing the future relationship once there has been "sufficient progress" on the divorce -- an estimated 100-billion-euro ($112 billion) exit bill, the rights of three million EU citizens living in the UK, and the border in Northern Ireland.
This week's talks are also set to address more detailed concerns such as Britain's future in Euratom, the EU's nuclear safety agency, and the role of the European Court of Justice, the EU's top court.
EU leaders are set to decide at a summit in October whether there is enough common ground to move on to trade talks.
Common ground was very much lacking last week after British foreign minister and leading Brexiteer Boris Johnson remarked that the EU could "go whistle" over its massive Brexit bill demand, drawing a rebuke from Barnier.
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