George W Bush has been sworn in for a second term as US president, and has vowed to support those who work to overthrow tyranny around the world.
Bush's speech sounded like a call to arms, analysts say
"The survival of liberty in our land increasingly depends on the success of liberty in other lands," Mr Bush said.
He promised to "strive in good faith" to heal divisions inside America.
The BBC's Matt Frei says many Americans will be sceptical about the cost and success of Mr Bush's liberty agenda, including some of his own supporters.
An estimated 500,000 people braved the snow and the cold for the $40m (£21m) ceremony and the traditional parade - some to protest against Mr Bush's policies.
There was unprecedented security across Washington DC for the inauguration - the first after the 11 September 2001 attacks.
But one protester managed to get within about 150m of the stand, shouting: "Hey Bush where are the poor? Did you ship them off to war?"
Mr Bush took the oath of office outside the Capitol building using a family Bible - moments after his Vice-President Dick Cheney was sworn in, in accordance with the US constitution.
He said that "ideologies that feed hatred and excuse murder" constituted "a mortal threat" and only one force of history could break that - "the force of human freedom".
"The best hope for peace in our world is the expansion of freedom in all the world," Mr Bush told the gathering.
It is the policy of the US, he said, to support forces of democracy "with the ultimate goal of ending tyranny in our world".
The US president had stern words for US allies - good relations with the US "will require the decent treatment of their own people", he said.
The BBC's Rob Watson in Washington says that, unlike four years ago, the president begins his second term after a comfortable election victory, but he still faces many challenges.
The war in Iraq is increasingly unpopular and opinion polls suggest Mr Bush's overall approval ratings are lower than any other re-elected president in recent years.
That rating currently stands around the 50% mark - the lowest for a returning president since Dwight Eisenhower in 1957.
Some protesters were arrested at the event
Mr Bush told the audience: "We have known divisions, which must be healed to move forward in great purposes - and I will strive in good faith to heal them."
And he called on Americans to " abandon all the habits of racism, because we cannot carry the message of freedom and the baggage of bigotry at the same time".
Security measures for the inauguration were intense.
About 6,000 police and 7,000 military personnel were on duty for the inauguration, alongside an undisclosed number of secret service personnel. Snipers had taken up positions on rooftops.
Manhole covers on Pennsylvania Avenue - the route of the parade - had been welded shut as a precaution.
A number of "counter-inaugural" events were staged, including an anti-war march through Malcolm X Park.