Almost exactly a year after Britain's seismic referendum to leave the bloc, the EU's chief negotiator, Michel Barnier of France, welcomed his counterpart David Davis with a cheery handshake at the European Commission in Brussels.
The smiles belied the fact that at stake is not just Britain's future but also Europe's postwar political order and its place in the world, which could be fatally undermined without an agreement by the March 2019 deadline.
"I hope today we can identify priorities and a timetable that would allow me to report to the European Council (summit) later this week that we had a constructive opening of negotiations," added the former European commissioner and French foreign minister, speaking against a backdrop of British and EU flags.
A key issue he did not mention was the EU's bill for Britain to leave, which Brussels estimates at a colossal 100 billion euros.
Davis, a prominent tough-talking figure in the "Leave" campaign, sounded a positive note, saying that while there would "undoubtedly be challenging times ahead" he wanted a good relationship with the EU.
"There is more that unites us than divides us", Davis said, referring to the latest reported terror attack overnight in London and the loss of lives in forest fires in Portugal.
"We launch negotiations in a positive and constructive tone, determined to build a strong and special partnership between ourselves and our European allies and friends in the future."
European stocks rose today, partly on optimism about the talks actually getting underway after months of sniping and uncertainty, analysts said.
In Berlin, German Chancellor Angela Merkel emphasised the unity of the remaining 27 EU countries, who have been alarmed in recent weeks by May's threats to walk out of the talks.
"I would like us to get a good agreement that is in both sides' interests. But the 27 of us will formulate our interests very clearly and hopefully, together," Merkel said.
Worried by immigration and loss of sovereignty, Britons voted last year to end their country's four-decade membership in the 28-country bloc -- the first nation ever to do so.
The vote came as a profound shock to Brussels against a backdrop of rising anti-EU sentiment, with many -- including now US President Donald Trump -- predicting the bloc's eventual break-up.
May officially triggered the two-year Brexit process in March when she was riding high in opinion polls, and called for fresh elections shortly afterwards to shore up her mandate for a tough Brexit stance.
But instead she lost her parliamentary majority, putting that hard-line approach and her political future in doubt after the disastrous June 8 election.
Britain now appears to have given in on the EU's insistence that the negotiations first focus on three key divorce issues, before moving on to the future EU-UK relationship and a possible trade deal.
Those issues are the exit bill; the rights of three million EU nationals living in Britain and the one million Britons on the continent who currently are allowed to live, work and claim welfare benefits; and the status of the border between Northern Ireland and Ireland.
May herself will also have a chance to update the other 27 EU leaders on her Brexit plans at a summit meeting in Brussels on Thursday.
"The best way we can spend this week is to rebuild trust," rather than tackle the big difficult issues right at the start, a European source said.
After the initial shock of last year's Brexit vote, the bloc at 27 appears to have steadied in recent months and got a real morale boost with the election of French President Emmanuel Macron in May.
Macron, a committed pro-EU leader and ally of Merkel, also easily won French legislative elections on Sunday, cementing his power base.
But many in Brussels fear that London has no real strategy, with May under pressure at home and still trying to close a deal with a conservative Northern Ireland party to stay in power, and facing criticism for her handling of the aftermath of a devastating tower block fire.
Finance minister Philip Hammond confirmed Sunday that it was still the plan to quit not only the EU but the customs union and the bloc's single market as well.
But he warned that "we need to get there via a slope, not via a cliff edge".
Barnier has warned that the negotiations must be wrapped up by October 2018 to allow time for all parties to ratify a final accord by March 2019.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)