At White House Summit, a Master Class of Diplomacy. In Courting Trump.

Over the course of the last seven months, the leaders of the Western world have been enrolled in an intensive course of Trumpology. One by one, presidents and prime ministers of European countries have traveled to Washington, learning all sorts of lessons about how best to handle the tricky man who sits behind the big desk in the gold-wrapped room shaped like an Oval.

On Monday, the whole class showed up at the White House. The time had come to put their education to use. And it was the Ukrainian leader, Volodymyr Zelensky, who seemed to have learned the most since his last visit, when he was mocked for not wearing a suit, deemed insufficiently deferential and ultimately kicked out.

This time he showed up to his Oval Office meeting with a more formal look, a game sense of humor and a letter for the first lady.

“I cannot believe it,” Mr. Trump said as he looked Mr. Zelensky up and down, taking measure of his new black-on-black get-up. “I love it. Look at you.”

In the Oval Office, Mr. Zelensky again encountered Brian Glenn, the right-wing reporter-instigator who had criticized Mr. Zelensky for his clothing the last time he was in the Oval. Mr. Glenn told Mr. Zelensky that he “looked fabulous” now. Mr. Zelensky played along: “You are in the same suit. You see, I changed, you have not.” Everybody laughed.

The Ukrainian president produced a letter from his wife addressed to Melania Trump. Mr. Trump seemed thrilled by this. “It’s not to you, it’s to your wife,” Mr. Zelensky said as Mr. Trump took the letter in hand. This caused Mr. Trump to laugh and smile wide. “I want it!” he said.

Later in the afternoon, Mr. Trump and Mr. Zelensky joined the leaders of Britain, Germany, Italy, France and Finland in the State Dining Room. The NATO secretary general, Mark Rutte, and the president of the European Commission, Ursula Von der Leyen, were there as well. Both had at various times earlier in the year found their own methods for dealing with Mr. Trump. Now they sat together and tried to work him as one.

Around the table they went, thanking him for all that he had done while ever so gently slipping in their specific pleas for a lasting security guarantee in Ukraine and an immediate cease-fire.

This delicate dance seemed momentarily at risk when the German chancellor, Friedrich Merz, insisted a bit more forcefully than the others that a cease-fire was of paramount importance. Mr. Trump had gone to Alaska days earlier with the stated aim of achieving a cease-fire, but after he failed to get one, he changed his tune. His public position now is that a cease-fire is not necessary to continue with negotiations. When Mr. Merz insisted that the opposite was the case, the smile left Mr. Trump’s face.

Nails on a chalkboard. Someone had upset the president. He got defensive for a moment, but then the meeting started to hum along at a pleasant pitch once more.

The European leaders in the State Dining Room were there to manage a global crisis. Which meant they also had to manage the mood of one famously mercurial man. The subject of this high-level diplomatic summit was diplomacy mixed with psychology.

Adding to the surreal nature of the thing was the way that President Vladimir V. Putin of Russia hovered over it all, just out of sight, like a character offstage. Mr. Trump kept bringing up Mr. Putin’s perspective. “Vladimir Putin wants it to end,” he claimed. He repeatedly mentioned that he needed to call Mr. Putin to update him on how the meetings were shaping up.

The Europeans looked stoic at every mention of Mr. Putin, as though they hardly needed to be reminded of the Russian leader’s viewpoint.

Who has better mastered the technique of appealing to Mr. Trump’s sensibilities, Mr. Putin or the Europeans? After the Russian leader got his face time with Mr. Trump at their summit in Anchorage on Friday, the American president came away having adopted much of Mr. Putin’s approach on Ukraine.

But by Monday’s end it did seem as though the Europeans had learned a thing or two.

“I had a very good meeting with distinguished guests,” Mr. Trump wrote on social media after it was all over.