Vladimir Putin has been inaugurated as president of Russia in a ceremony in the capital, Moscow.
Mr Putin is returning to the presidency after an absence of four years in which he served as prime minister. The outgoing President, Dmitry Medvedev, was widely seen as an ally of Mr Putin.
He won a third term as president in controversial elections in March.
On Sunday, thousands of protesters opposed to the inauguration clashed with police in Moscow.
Mr Putin took the presidential oath at the Grand Kremlin Palace, in a hall that was once the throne room of the Russian tsars.
In a short speech he said Russia was "entering a new phase of national development".
"We will have to decide tasks of a new level, a new quality and scale. The coming years will be decisive for Russia's fate for decades to come."
He said Mr Medvedev had given a new impulse to modernisation, and the "transformation" of Russia must continue.
He also spoke of the need to strengthen Russian democracy and constitutional rights.
If he completes his six-year term, Mr Putin will be the longest serving Russian leader since Soviet supreme ruler Joseph Stalin, our correspondent says.
However, Mr Putin faces many problems; the political system he created has been showing cracks, economic growth is forecast to slow, and violence in the volatile North Caucasus continues, he adds.
How Mr Putin deals with the wave of opposition protests which broke out last December will also be a key test of his administration, correspondents say.
Sunday's protest against the inauguration was peaceful until a small group of demonstrators tried to break through the lines of riot police.
Some of the protesters launched a sit-in by the police lines, refusing to leave unless the inauguration was cancelled.
They were also demanding an hour of TV airtime and new elections.
Prominent opposition activists Alexei Navalny, Sergei Udaltsov and Boris Nemtsov were among dozens detained.
A rival demonstration in support of Mr Putin also took place in the city.