Henry A. Kissinger, the scholar-turned-diplomat who engineered the United States’ opening to China, negotiated its exit from Vietnam, and used cunning, ambition and intellect to remake American power relationships with the Soviet Union at the height of the Cold War, sometimes trampling on democratic values to do so, died on Wednesday, according to a statement that was posted to his official website.

He advised 12 presidents — more than a quarter of those who have held the office — from John F. Kennedy to Joseph R. Biden Jr. With a scholar’s understanding of diplomatic history, a German-Jewish refugee’s drive to succeed in his adopted land, a deep well of insecurity and a lifelong Bavarian accent that sometimes added an indecipherable element to his pronouncements, he transformed almost every global relationship he touched.

There was something fundamentally simple, if terrifying, in the superpower conflicts he navigated; he never had to deal with terrorist groups like Al Qaeda or the Islamic State, or a world in which nations use social media to manipulate public opinion and cyberattacks to undermine power grids and communications.

It was Mr. Kissinger’s task to turn that promise into a reality, and he made clear in a Foreign Affairs article, published as Nixon was preparing to take office, that the United States would not win the war “within a period or with force levels politically acceptable to the American people.”

As Mr. Kissinger sat with his big yellow legal pads in his White House office, scribbling notes that have now been largely declassified, he designed a three-part plan: A cease-fire that would also embrace Laos and Cambodia, which had been sucked into the fighting; simultaneous American and North Vietnamese withdrawals from South Vietnam; and a peace treaty that returned all prisoners of war.

It was the bombing campaign in Cambodia — code-named “Operation Menu,” with phases named “Breakfast,” “Lunch” and “Dinner” — that outraged Mr. Kissinger’s critics and fueled books, documentaries and symposiums exploring whether the United States had violated international law by expanding the conflict into a country that was not party to the war.

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