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8 year oldFrance's Le Figaro declares that "Theresa May will be the prime minister of Brexit. Deeply divided by the referendum on Europe, the Conservative Party reunites - at least it seems so - behind her and this objective, in a life-saving reflex."
A commentary in the left-wing French paper L'Humanite says Tory heads have been "spinning" ever since the victory of the Brexit camp, but the party can now pick itself up and carry on.
The Brussels correspondent of the German broadcaster Deutsche Welle believes that while Mrs May inherits an unenviable legacy from her predecessor, she is an experienced enough politician to be able to ride out the storm. Barbara Wesel says: "At least Britain and the rest of Europe now get a professional politician, not a fanatic. That is in itself good reason for being a little grateful."
Frankfurter Allgemeine Zeitung's politics editor, Peter Sturm, takes a similar line, saying the choice of Theresa May provides some clarity for Britain and the European Union. He also cautiously welcomes the fact that she has not so far adopted any "extreme positions".
However, Spiegel Online declares that Mrs May "is considered to be cool but also to thrive on conflict. She may need this, as Brussels will now lay on the pressure."
Some European commentators make comparisons between Theresa May and other strong female leaders such as former British Prime Minister Margaret Thatcher and German Chancellor Angela Merkel.
Thomas Kielinger, writing in the German daily Die Welt, says Mrs May shares with both women an aversion to "small talk and media chatter".
The Italian daily Corriere della Sera describes Mrs May as "a bit of Merkel, a bit of Thatcher" and notes that she "is reputed to be an uncompromising politician".
Riccardo Scarpa, writing for Italy's Il Tempo, notes that with her declaration "Brexit is Brexit", Theresa May set out her stall "with the enthusiasm and determination of a woman who has already been dubbed the new Thatcher".
However, Sueddeutsche Zeitung's London correspondent Christian Zaschke believes Mrs May is unlikely to become a second "Iron Lady", as she is more of "a pragmatic Conservative who occasionally borrows some ideas from the Left".
The Iron Lady tag is perhaps inevitably seized on by a number of media outlets beyond the bounds of the EU too.
Several Russian TV channels, including the state-controlled Channel One and the rolling news channel Rossiya 24, speculate on whether Theresa May will become a "second Iron Lady" - a preoccupation echoed by the state-owned dailyRossiyskaya Gazeta and the business daily Vedomosti.
USA Today is in no doubt over Mrs May's right to the title of Iron Lady. The paper says "the United Kingdom is about to usher in a leader who is every bit as formidable and steady as the last woman who ran the country: Margaret Thatcher".
It adds that like Mrs Thatcher, Theresa May "has a reputation for steely determination and a willingness to stand up to the men who traditionally dominate British politics".
Mrs May's taste in footwear - already a favourite topic in the British media - also comes under scrutiny. The German tabloid Bild homes in on her famous leopard-skin patterned shoes, while a headline in Spain's El Mundo lists her qualities as "high heels, firm step, absolute control, total loyalty".
A headline in Italy's Corriere della Sera also refers to Mrs May's "stiletto heels".
But the Italian news agency Ansa refuses to succumb to the hype, saying that while Mrs May has "a passion for shoes", these are "strictly with low heels, up to a maximum of five centimetres".
Ansa adds for good measure that "sexist comments aside, when you hear her speak today, you can bet that Theresa's main concern is neither the criticism of journalists nor the comparison with Merkel".
BBC Monitoring reports and analyses news from TV, radio, web and print media around the world. You can follow BBC Monitoring on Twitter and Facebook.
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