A new New Deal?:Titanic deficits, rising unemployment, tumbling house prices and a frozen financial system mean that the new president's most urgent task is to shore up and revive his country's shrinking economy.
Barack Obama and his Democratic allies in Congress favour pumping billions into the economy with a massive economic stimulus package that will target lower- and middle-income households, but falling tax revenues could inhibit their room for manoeuvre.
Hello again, world:
After eight years spent threatening or boycotting its enemies and bullying or ignoring its allies, the US is ready to embrace diplomacy again. Obama's promise to withdraw from Iraq will please allies but he is demanding that Europeans should share more of the military burden in Afghanistan.
Next April's summit of the North Atlantic Treaty Organisation will consider again the admission of Georgia and Ukraine, presenting the new president with the first test of his influence over European allies and his approach to US-Russia relations.
A comeback for the constitution:
Obama has promised to examine every executive order signed by George Bush and to reverse any expansion of presidential power he deems constitutionally questionable. He will also stop torturing suspected terrorists and shut down the detention centre at Guantánamo Bay, but he must first decide what to do with those currently held there.
Some Democrats in Congress want to prosecute former Bush officials for abuses of power, but Obama's more cautious allies fear such a move could undermine his promise of a bipartisan approach to government.
Healthcare for all, maybe:
The US has the most expensive healthcare system in the world, but 47 million people have no coverage and many more are inadequately insured. Obama has promised to extend the federal employees' health plan to all Americans who want it, but the proposal is expensive and will face fierce resistance from the health insurance industry.
Obama's plan does not require everyone to take out health insurance, raising fears that many will remain outside the system, pushing up costs for everyone else.
Spreading the wealth around:
Republicans branded Obama a socialist when he suggested that growing inequality in America was an economic as well as a social problem. The new president has vowed to increase taxes on the richest 5 per cent and to ease the tax burden on everyone else.
Tackling structural inequality will be more difficult, requiring among other steps a dramatic improvement in the education available to poor Americans. African-Americans know that electing a black president will not transform their lives immediately, but they hope he will understand their concerns better than his predecessors.
Tackling climate change:
Investing in alternative energy sources and reducing the US dependence on imported fossil fuels could help to reduce carbon emissions. Obama will not seek to revive the Kyoto protocol, but has promised to lead a new international effort to combat climate change that would include big developing countries such as China and India.