In this June 19, 2017 photo, Britain's Prime Minister Theresa May speaks to the media outside 10 Downing Street in London.
Barnier has said a divorce deal should be ready by October next year to give time for parliamentary approval.
"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.
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.
Still, British Foreign Secretary Boris Johnson remained upbeat Monday and thinks that the Brexit negotiations will yield "a happy resolution that can be done with profit and honour for both sides". It left an image of a dysfunctional Britain coming up against a well-oiled European Union negotiating machine. European Union diplomats hope this first meeting, and a Brussels summit on Thursday and Friday where May will encounter but not negotiate with fellow European Union leaders, can improve the atmosphere after some spiky exchanges.
Such criticism would have been unthinkable before the June 8 election, in which the Labour Party under Jeremy Corbyn capitalized on its opposition to austerity cuts, leaving May scrambling to shore up a minority government.
A year after its historic vote, Britain on Monday finally opened negotiations with the other 27 European Union nations about leaving the bloc, with the final outcome, due in 2019, as globally important as it now seems unpredictable. Here's a look at the people who are likely to dominate these talks over much of the next two years. 'Put the economy first'They point out that their organisations represent hundreds of thousands of businesses across the United Kingdom, employing millions of people, and say the business community fully accepts the voters' decision in last year's referendum to leave the EU.
Eurocrats in Brussels were today told they can go home early if they get too hot - despite tough Brexit negotiations kicking off.
Saif Ali Khan praises Karan Johar, says Bollywood is incomplete without him
However, as one would expect, no, Saif did not play any role in helping Sara decide her Bollywood debut. Though Saif is a little skeptical, he revealed that Sara always wanted to be an actor.
Her pro-EU party won 12 seats at the shock General Election which saw no party with a clear majority and the Conservatives the largest party overall.
Other issues to be discussed include future arrangements on security co-operation and intelligence sharing once Britain is outside the structures of the EU. What was surprising was May's decision to appoint a man known for his countless gaffes as her country's top diplomat. He added: "I think the Prime Minister has got us into a complete mess". This date can be extended by agreement between all member states.
A mountain man from France's southeast, he made a name for himself as co-president of the 1992 Albertville Winter Olympics.
Other European parliaments could also hold votes on any agreement.
The UK could fall back on World Trading Organisation default tariffs under a hard-Brexit "no deal", making multi-national firms' exports more expensive to buyers in the bloc.
"Now, we have a shared responsibility to deliver quick and substantive progress".
Be Civil - It's OK to have a difference in opinion but there's no need to be a jerk.