She was admired, even doted upon, by American presidents, and detested by many leaders of African states. But no-one, least of all her critics, ever treated her as of no consequence.
Perhaps the most difficult world leader, from her viewpoint, was the late Indira Gandhi. Their meetings in Delhi seemed to prove the theory that powerful women, although happy to deal with their equals if male, simply cannot do business together.
Once they emerged from what was obviously a fiery meeting in the Indian capital "with sparks coming out of their heads", to quote a witness at the time.
The people of Moscow, especially during the Cold War, adored her, but Soviet leaders treated her warily. Shortly after she swept to power in 1979, Leonid Brezhnev scoffed in the Kremlin: "She is trying to wear the trousers of Winston Churchill." He soon learned to treat her with less disdain.
But her Kremlin favourite was Mikhail Gorbachev, the man she famously could do business with.
Unlike his grim predecessors, Mr Gorbachev would debate intelligently. She loved it.
Their meetings were once summed up like this: "Like an English summer's day - thunderstorms and sunny periods."
Sir Bernard Ingham, her press secretary, said the chemistry between the two leaders was "quite extraordinary". Mr Gorbachev's wife, Raisa, even appeared to some observers to be jealous.
The Soviet press treated her less kindly. Headlines such as "The Cold War warrior" and "The Wicked Witch of the West" screamed across their front pages.
But it was Red Star, the Soviet army newspaper which did her the biggest favour, although unintentionally, describing her as "The Iron Lady".
Later she was to say: "The Russians said I was an Iron Lady. They were right. Britain needs an Iron Lady."
Across the world was US president Ronald Reagan, who doted on Mrs Thatcher. The feeling was reciprocated and during this period the so-called special relationship between the UK and the US was particularly warm.
In 1983, he said of her: "She is the best man in England."
Her response was fulsome: "America's successes will be our successes. Your problems will be our problems. When you look for friends, we will be there."
Mr Reagan's successor, George Bush senior, was cooler towards Mrs Thatcher, but insisted, nevertheless, that the "special relationship" remained as special as ever.
But it was perhaps in Europe that she left the biggest impression. Her critics to this day accuse her of handbag diplomacy, foghorn diplomacy and high-octane diplomacy. But her table-thumping and shouting had its effect.
Francois Mitterrand, as the president of France, once said of her: "She has the eyes of Caligula, but the mouth of Marilyn Monroe."
Another French president, Giscard d'Estaing, liked her at first, but grew colder because she invariably got the better of him.
Helmut Schmidt, the West German chancellor, described her as "no soft touch" - a considerable understatement.
A different German chancellor, Helmut Kohl, found her altogether overwhelming. Once when they were together in Germany, Mr Kohl pleaded another urgent engagement and made good his escape. A short while later, Mrs Thatcher reportedly spotted him scoffing cream cakes in a nearby cafe.
Meanwhile, Henry Kissinger, the US secretary of state, thought she was "quite a girl".
But her view of another US secretary of state, Al Haig, who was operating during the Falklands conflict, was that he was "woolly" and "timid". He was plainly awestruck by Mrs Thatcher because after he returned to his suite in Claridges following a tumultuous meeting with her, he cried out: "Somebody get me a drink - and fast. That's one hell of a tough lady."
She did not trust Mr Haig. One aide said: "She was certain that he was fully capable of stabbing her in the back with a middle-of-the-night deal with the Argentines for his own glory.2
What the world admired about Mrs Thatcher - not that they necessarily liked it - was that she would not temper her views, or soften her opinions, or patronise those whose views were the antithesis of hers. If you were not "one of us", you got it in the neck.
Only once did she find, to her dismay, an audience which was visibly underwhelmed by her presence.
She was forced to meet a group of unsmiling workers when her plane landed in the snowy wastes of Siberia to refuel. The conversation lagged. To perk it up, she asked them whether they would like signed photographs of her.
"Nyet!" they cried in a single voice. Perhaps only Siberian trade unionists would have dared...
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