By Paul Reynolds
World Affairs correspondent, BBC News website
On his visit to Europe this week, US President George W Bush will seek to make friends, but will have trouble influencing people.
Bush is in a stronger position after his re-election
Despite his charm offensive, there are too many issues dividing the US from much of Europe to enable peace to be declared on all fronts.
Nevertheless, there will be efforts towards finding a way forward on some of these problems, though some of this is papering over the differences.
On Iraq, Mr Bush will seek, and probably get, assurances that the Europeans will do more to train Iraqi security forces who are to bear a major burden in fighting the insurgency.
Sunday: Arrives in Brussels
Monday: Talks with Belgian leaders, then gives speech on transatlantic relations. Dinner with French President Jacques Chirac
Tuesday: Breakfast with UK Prime Minister Tony
Blair. Meets Ukrainian and Italian leaders at Nato HQ, then meets European Union leaders then holds news conference
Wednesday: Leaves Brussels for Germany. Holds news conference with Chancellor Gerhard Schroeder in Mainz, then meets US troops in Wiesbaden. Leaves for Slovakia
Thursday: Gives speech in Bratislava, meets Russian President Vladimir Putin, then holds news conference
On China, the European Union will seek to reassure Mr Bush that a general code of conduct on arms sales will restrict transfers, even if the specific embargo on China is lifted.
He might not be convinced.
On Iran, the US will give time for European negotiations about Iran's nuclear programme to conclude this year. But what happens if the talks fail?
On the Middle East, all can rally in support of peace talks and in support of a Syrian withdrawal from Lebanon.
Mr Bush also wants the Lebanese group Hezbollah declared a terrorist organisation, but not all Europeans agree.
In other areas, climate control and the International Criminal Court, for example, the differences are stark and demonstrate the policy gap.
There is always, of course, a list of transatlantic problems.
But such are the underlying differences these days, that some people think a process of realignment is beginning, in which Europe begins to emerge as an entity and potentially as a rival.
If that is the case, the future of transatlantic diplomacy will be less to seek harmony and more to accept competition.
Bush's tour takes in "old" and "new" Europe
Europeans would make a mistake if they underestimated Mr Bush's confidence.
He is in a much stronger position than a year ago.
He has been re-elected, voting has taken place in Iraq, there is movement on the Israeli-Palestinian front and he has armed himself with a world view.
He declares that he has, as he put it, "firmly planted the flag of liberty" in Iraq and hopes to do so elsewhere.
In comments on Thursday, he made it clear this would be a theme of the visit.
"Part of my reason I'm going to Europe is to share my sense of optimism and enthusiasm about what's taking place [in Iraq] and remind people that those values of human rights, human dignity, and freedom are the core of our very being as nations," he said.
It is interesting to note how the elections have enabled Mr Bush, and UK Prime Minister Tony Blair, to shift the perception of Iraq.
They now present the elections as their success - and the violence as primarily now an inter-Iraqi conflict.
For their part, many of the European leaders - though not all, for Mr Bush does have some admirers - will want to see evidence that he is willing to listen as well as talk.
Certainly, Mr Bush is covering all the bases. Not only is he going to Nato, but he is meeting all the European Union leaders at a special European Council as well.
It is recognition of European institutions, though it is also perhaps a way of hinting that it takes all of them to equal one of [Mr Bush]
This will be a first for a US president and it is a sign that former US presidential adviser Henry Kissinger's complaint about there being no one telephone number for Europe is no longer so valid.
It is recognition of European institutions, though it is also perhaps a way of hinting that it takes all of them to equal one of him.
Mr Bush is also having sessions with his three main opponents over the Iraq war.
There is a private dinner for the French President Jacques Chirac, a visit to Germany for German Chancellor Gerhard Schroeder and a summit, albeit in Slovakia, for Russian President Vladimir Putin.
Each meeting will present a problem.
Mr Chirac wants what the French call a "multi-polar" world, not one dominated by the United States.
There is however a common interest in Lebanon and in getting Syrian troops out.
Mr Schroeder is showing further signs of dissent from Washington.
He has just floated a proposal to set up a high-level panel to review the future of Nato.
Nato, he complained, had ceased to be "the primary venue where transatlantic partners discuss and co-ordinate".
Relations between the US and Russia have not been easy
The speech was seen as a pointer towards a greater role for the EU.
When the idea came out at a conference in Germany, the US Defense Secretary Donald Rumsfeld simply ignored it.
Yet the idea does reflect what sooner or later must be faced - how long will Nato survive and even how long will US troops be in Europe?
As for Mr Putin, he has his problems, but he has been a disappointment for the Americans.
Mr Bush is expected to raise the increasing evidence of Russian authoritarian tendencies. He said he would do so with such leaders in his inaugural speech in January.
The meeting is not expected to be particularly cosy, especially as Russia seems to believe Iran's assurances that it will not build a nuclear bomb.
Call for compromise
An indication as to how seriously divisions between the US and Europe must be taken has come in a document issued by a US think-tank in advance of the visit.
Signed by 50 foreign policy professionals from both sides, the Brookings Institute's document, called "A Compact between The United States and Europe", goes beyond the usual waffle in these kinds of papers.
It offers specific proposals for the various policy issues of the day and calls for compromise all round.
It declares: "American policies spark hostility among Europeans, or vice-versa. That hostility, in turn, convinces leaders on both sides that they have no choice but to go it alone. This vicious cycle benefits no one and must stop."
The "compact" adds: "In recent weeks, optimism has grown that the partnership can find new vitality. But renewal requires more than hope; it requires action".