(CNN) -- Europe's expectations of a Barack Obama presidency are vibrant, vast and probably incapable of fulfillment by any president, let alone one who will come to office in the middle of a worldwide economic crisis and with huge, unfinished business in Iraq and Afghanistan.
Europe wants to have something to love about America again.
There is no doubting the buzz and the optimism that the election victory of an African-American candidate has brought.
Most in Europe are instinctively America's friends and, after the unilateralism of the Bush years, they want to have something to love about America again.
Obama's arrival, they hope and believe, will give them that opportunity.
President-elect Obama's brilliant rhetoric, which has electrified crowds at home and reached many not previously interested in politics, has appealed to European instincts.
Europeans tend mostly to identify with the leftish end of the American political spectrum. Europeans want change in America and in the world and they see Obama as a purveyor of change.
As the former British Foreign Secretary Malcolm Rifkind put it during the campaign: "It's a touch of the John F. Kennedys and the Camelot-type excitement. That doesn't necessarily mean it's healthy. It doesn't necessarily mean it's justified -- but it's a product of Obama's personality."
Europeans will hope especially for President-elect Obama to repair some of the dents in America's image which have reflected on them too. They want and expect to see Guantanamo Bay closed down for good. They want an end to the use of so-called "extraordinary rendition" -- the soft name for what has, in effect, been kidnapping and torture by the CIA -- that has besmirched the name of democracy.
Part of Obama's street cred in Europe is that he opposed the war in Iraq from the outset. Europeans hope that he will prove less ready than George W. Bush to use America's vast military force as an instrument of foreign policy.
They hope he will engage with them, for example, in diplomatic rather than military methods to wean Iran away from the development of a nuclear weapons program. They hope he is readier to accept the Churchill doctrine of jaw, jaw being better than war, war.
They are looking for new thinking, for a president ready to step out of the box. While Obama was slogging it out for the Democratic nomination with Hillary Clinton, Denis Macshane, a former Europe Minister in the UK Labour government, put it to me like this: " I would hope the next administration can open doors to Iran. If President Nixon, a right-wing republican can go to Communist China, then why can't the next presidency say: 'I don't like Iran but we are going to have normal diplomatic and trading relations with them'. Ditto on Cuba. Put away the leftovers of the 20th Century."
High hopes. But Obama too has security concerns for his country. Obama too, as his campaign speeches in carefully chosen quarters showed, is subject to the pressures of the powerful Israeli lobby in U.S. politics.
Europeans should remember that what he said in 2002 was "I am not opposed to all wars. I am opposed to dumb wars."
Reverse the order of those two sentences and you get a slightly different picture. "I am opposed to dumb wars...I am not opposed to all wars."
The U.S. and Europe share many values. But they don't always share interests.
During the campaign Obama told us on Iraq: "I will give our military a new mission on my first day in office. Ending this war." And while European diplomats know that the 150,000 U.S. troops in Iraq won't be coming home immediately they would like to be given some more specifics from him in office about when it will be.
Europeans sense too that they may find an Obama administration even more forceful than the Bush White House in demanding that Europe puts more resources and troops into Afghanistan. That has become Obama's cause. As Robin Niblett, the director of think tank Chatham House, warned during the campaign: "His commitment to Afghanistan is highly important for the British government and a source of concern potentially for the French or Germans who do not want to put as many troops in as he is likely to ask for."
As Obama's own writings make clear, he believes that America must be free to take unilateral action on occasion. It may have to act occasionally as the world's high sheriff. But what Europeans hope is that President-elect Obama will prove to be instinctively multilateralist, that he will make full use of the United Nations, that he will at least consult and listen to them.
George W. Bush didn't even pretend to do so during his first four years and paid the price. Then he and Condoleezza Rice decided to play it differently during the second four years, and won much more co-operation from Paris and Berlin and London as a result.
Although Europeans are having their own struggles now balancing their urge to counter climate change with their efforts to avoid recession and slump they really do hope that President-elect Obama will live up to his promises to make America a leader in saving the environment.
After all, he did tell us that his election would mark the moment "when the rise of the oceans began to slow and our planet began to heal." Europe will be looking for him to create those promised five million new jobs in the clean energy sector, those one million plug-in hybrid cars on the road by 2015.
But will he go ahead with his plans for a cap and trade system to reduce carbon emissions? Will he lead the world in agreeing a follow-up to the Kyoto agreement limiting greenhouse gases? Amid the economic confusion that will be an essential early test of whether Obama's achievements will live up to his rhetoric.
One issue though will worry the Europeans about President-elect Obama. During the campaign he frequently gave indications of a protectionist stance on trade issues. A Europe struggling to revive economic activity after suffering in the aftermath of a largely American-induced economic crisis will not thank him if he puts up the barriers and puts American interests first last and everywhere else in trying to protect the victims of a false economy built by those who speculated too wildly on borrowed money.
He may have to look first to domestic issues but he has been elected unofficial leader of the free world too and open American markets are essential to world recovery.