The second round of Brexit negotiations will take place in Brussels on Monday, the British government said Friday.
The three negotiating groups cover citizens' rights, the financial settlement between the two parties and other separation issues.
Issues relating to Northern Ireland and the governance of the withdrawal agreement are to be addressed by the coordinators.
The coordination and negotiation sessions go on through the week until a closing plenary and a press conference on Thursday.
The EU says it will only start discussing future relations with the UK, including a possible trade deal, after "sufficient progress" has been made on these opening topics, hopefully later this year.
The exit bill has been a major source of contention.
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.
British Prime Minister Theresa May's government published a draft law Thursday to formally end Britain's membership of the EU, but opposition parties and the leaders of Scotland and Wales threatened to block what they called a "naked power-grab".
The new bill would repeal the 1972 European Communities Act, convert an estimated 12,000 existing European regulations into British law and end the supremacy of EU legislation.
"This bill means that we will be able to exit the European Union with maximum certainty, continuity and control," Davis said.
But ministers are braced for a battle over provisions that give them new powers to amend the EU laws as they are transferred without full parliamentary scrutiny.
On June 23 last year, Britons voted by the narrow majority of 52 percent to 48 percent to leave the European Union, ending four decades of membership of the continental fold