"One of them of course ... is the Brexit negotiations, those have started formally today so we've put in place the work to enable us to reach that deep and special partnership with the European Union that we believe is not just in our interests but also the interests of the European Union for the future".
"We want both sides to emerge strong and prosperous, capable of projecting our shared European values, leading in the world, and demonstrating our resolve to protect the security of our citizens".
- October 19 - Mr Barnier is set to report back to the EU27 on whether sufficient progress has been made to move on to phase two of the talks, covering the UK's future trade relationship with the remaining EU.
Sounding conciliatory, Britain's Boris Johnson said as he arrived at a meeting with fellow European Union foreign ministers in Luxembourg that he looked forward to "a happy revolution" in relations that would be good for Britain and the rest of Europe.
No. Except perhaps in agreeing a schedule for these talks and the separate strand of talks on "the future relationship" post-Brexit - ie trade.
The UK is reportedly planning to make a generous offer to the 3 million European Union nationals living in Britain so long as it's reciprocated for the 1 million Britons residing on the continent. Priorities drawn up at the EU's insistenceThe two other priorities on the initial agenda - drawn up at the EU's insistence - are how to maintain a "soft" border between Northern Ireland and the Irish Republic after Brexit, and the UK's financial obligations to European institutions and programmes.
The two men gave a joint press conference at the close of the first day of talks, held in Brussels and meant to identify priorities and a timetable for the negotiations. But a government spokesman in London said, "We believe that the withdrawal process can not be concluded without the future relationship also being taken into account".
So far, he has been successful in that job, making clear the European single market's "four freedoms", including free movement, are indivisible and forcing Mrs May to confirm her intention to pull the United Kingdom out to get control of immigration.
While "Brexiteers" like Davis have strongly backed May's proposed clean break with the single market and customs union, finance minister Philip Hammond and others have this month echoed calls by businesses for less of a "hard Brexit" and retaining closer customs ties.
Many in Britain have seen the election result as repudiating May's threats to walk away without a deal.
"It's a statement of common sense that if we are going to radically change the way we work together, we need to get there via a slope, not a cliff edge".
"No deal would be a very, very bad outcome for Britain, but there is a possible worse outcome and that is a deal that is deliberately structured to suck the lifeblood out of our economy over a period of time".
The EU says Britain must honour its contributions to the bloc's budget, which has already been agreed up to 2020, as well as commitments to development programmes for poorer member states.
Mr Hammond's warnings over Brexit were seized on by critics, with shadow chancellor John McDonnell claiming the Government is in "disarray".