But there is still considerable anger, especially in mainly Russian-speaking areas.
BBC correspondents report on the mood in cities across Ukraine.
Here in the large, north-eastern city of Kharkiv, there was some lawlessness on Saturday but everything is now back to normal.
There is, however, one exception: the central square - one of the largest in Europe - where a stand-off continues between those who back the Maidan protests and those opposed.
Each side has mustered some 200-300 supporters.
At one end of the square, the pro-Maidan activists took over the entrance to the regional administration on Saturday.
After scuffles with the pro-Russian protesters, they erected a barricade in a semi-circle around 15m (50ft) from the entrance.
The building also houses the regional parliament, city parliament and other institutions.
Immediately in front of the barricade is a protective line of police with shields.
On the opposition side of the square, some distance away, the pro-Russians surrounded the statue of Lenin with makeshift small barricades and lit fires, just as the anti-government protesters had done in Kiev.
On Monday, their opponents promised they would open the administration building for all officials but one - Kharkiv regional governor Mikhaylo Dobkin, who was appointed by the ousted president.
On Sunday he promised to return to work and said he would give a briefing at 09:00 GMT on Monday but postponed it without explanation.
Both he and the mayor were said to have fled, but the mayor, Gennady Kernes, said on Sunday he was willing to co-operate with the Kiev authorities for the sake of Kharkiv's citizens.
In Kiev, the cradle of the revolution, Monday dawned as a regular work day, after a weekend of earth-shifting events.
The metro is running, streets are clogged with cars, and businesses in the city centre are once again operating.
The capital is finally at peace.
But running beneath this return to relative normality is an uncertainty and disquiet over what will happen next.
Ukraine's new leaders are faced with a number of imperative tasks.
Not the least of these is the need to finish the formation of the government itself.
Interim President Olexander Turchynov must placate rumblings in the country's east and south, and somehow locate the fugitive Viktor Yanukovych, to prevent him from mounting any challenge to the new authorities.
Moreover, Ukraine is facing a five-alarm economic emergency.
According to Mr Turchynov, the country is on the verge of default.
Billions of dollars must be found. Now.
And while all this unfolds, eyes are glancing nervously east, to neighbouring Russia, which has now recalled its ambassador.
Moscow has a wide assortment of items in its toolbox, should it want to complicate the new government's existence - from a hike in gas prices to an economic embargo, to much worse.
But, above all, the new government must instil confidence that it is up to the job.
All Ukrainians are watching, transfixed.
But perhaps the group that is paying the closest attention is the Euromaidan activists, who still occupy Kiev's Independence Square.
They have now assumed a role similar to the ancient Roman forum, with an ability to influence the selection - and removal - of leaders.
If they are unsatisfied with how events develop, they have promised they will act.
And as we have already seen, they mean what they say.
There was no reply at The House That Viktor Built when I visited this morning.
One of the now ex-president's homes stands behind a huge wall on Raynisa Street in Donetsk.
The doorbell chimes but there's no response.
Rumours have swirled that Viktor Yanukovych tried to fly from Donetsk to Russia over the weekend but his plane was stopped by custom officers.
His support has ebbed even here - but this still remains his power base.
He was born just outside the city and was governor of the region.
This pro-Russian part of Ukraine looks east rather than west and won't take kindly to comments by interim President Oleksandr Turchynov that the country should move closer to Europe.
As light snow fell over Donetsk today, the mood was cautious.
One man, Sasha, told us he wouldn't mind reunification with Russia.
"We can't get along with the rest of Ukraine," he said.
But the majority seems to want to keep Ukraine together.
Even those demonstrating on the main square here in support of Russia and against the anti-government crowd in Kiev said they were for a united Ukraine - but one which respected all political sympathies.
The deep splits in this country have been laid bare these past few days.
And the challenge of uniting a polarised nation is a huge one.
Source: BBC News