The negotiations are set to start around June 19, with Britain set to leave the bloc by end-March 2019.
First up will be the status of European Union (EU) nationals resident in Britain, and of British citizens living elsewhere in the bloc. Both Labour and the Conservatives have said freedom of movement will end when Britain leaves the EU.
Since no party won an overall majority in the elections, there is little time to form a new government and get a negotiating stance up and running. Parliament meets next Tuesday to swear in MPs.
2 TERRORISM AND SECURITY
The general election was meant to be about Brexit but deadly terror attacks in Manchester and London, killing 30 people in all, changed the debate. The London Bridge attack was the third, after one on Westminster Bridge in March.
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Eighteen terror plots have been foiled since 2013 - five of them since March.
Mrs May came under pressure during the campaign for cutting thousands of police jobs when she was home secretary.
There were further questions when it emerged that some of the attackers were known to security services and apparently escaped the surveillance net.
Tackling the problem of radicalisation among British Muslims and militants returning home from Syria is likely to be a recurring theme for the incoming government.
Britain ran a Budget deficit of 2.6 per cent of gross domestic product (GDP) in March, down from 9.9 per cent in 2010 after the financial crash.
Its total public debt was £1.7 trillion (S$3 trillion) in April, or 86 per cent of GDP. Growth was 1.8 per cent, and inflation was 2.6 per cent.
Leaving the EU single market would give Britain the opportunity to strike its own trade deals outside the bloc.
The Conservatives pledged to eliminate the deficit and return Britain to profit by the "middle of the next decade", meaning further years of austerity.
Labour pledged to end austerity, hike corporation tax, raise taxes for the top 5 per cent of earners and eliminate the deficit in five years.
Scotland's governing Nationalists are pushing for a second independence referendum once the terms of the final Brexit deal start to become clear late next year or in early 2019.
Backed by the Greens, the separatists have the Scottish Parliament's support to ask the British government for formal powers to start the process.
If Labour required the backing of the Scottish Nationalists to form a government, it would likely come at the price of another referendum.
5 NORTHERN IRELAND
One of the most delicate parts of the Brexit negotiations will be the place of Northern Ireland within the United Kingdom, and relations with the Republic of Ireland, which will be the kingdom's only land border with the EU.
The likelihood of the UK being out of the EU single market, Customs union and the EU's free movement area could mean a return of a "hard border", which is fiercely opposed by local residents.
The 1998 accords that maintain the peace in the province after three decades of inter-community bloodshed are delicate, and there is concern Brexit could upset stability.
There is cur rently no sign that a majority in Northern Ireland, where pro-British Protestants remain the largest group, want a merger with the republic. But Irish nationalists Sinn Fein have called for a referendum on reunification within the next five years.