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Style, with substance: what’s really trending this week, a roundup of the best fashion journalism and your wardrobe dilemmas solved, direct to your inbox every Thursday

Footage captures the moment an eel escapes tail-first from the digestive tract of a predatory fish

In a video released by Kensington Palace, the Princess of Wales gives an update on her cancer treatment

Why has the far-right AfD party been so successful in Germany?

After weeks of arguments over the format and rules, the first presidential debate between Donald Trump and Kamala Harris took place in Philadelphia, Pennsylvania, a key swing state

In the rolling hills of central Italy sits Honeydew, an eco-community created as a direct response to the isolation of the Covid pandemic, enabled by modern technology and aiming to address the profound changes the climate crisis looks set to bring. With stated aims to spread the project globally, the Guardian visited Honeydew to see how founder Benjamin Ramm's vision for the future is playing out, and to learn how sustainable such eco living projects really are.

What does the feud between Elon Musk and Brazil’s supreme court mean for X and Starlink users in the country? Tom Phillips reports

Ian Sample and science correspondent Hannah Devlin discuss some of the science stories that have made headlines this week, from a new technique that uses food colouring to make skin transparent, to the first case of bird flu in a person with no known contact with sick animals, and a study looking at premature brain ageing in young people during Covid

The government saw off a rebellion over its plans to cut winter fuel allowance this week. John Harris speaks to Caroline Abrahams from Age UK about what this winter will look like for millions of pensioners losing out. Plus, he talks to columnist Rafael Behr about whether the technocrats (Starmer and Reeves) are taking the Labour party in the wrong direction

Max Rushden is joined by Barry Glendenning, John Brewin and Jonathan Fadugba to preview the first round of Premier League fixtures after the international break, including the north London derby

Rory Carroll and Helen Pidd meet the Kabin Crew and the Lisdoonvarna Crew – creators of a song that has notched up over a billion plays on TikTok – as they perform at the Electric Picnic music festival

This summer, one of my lectures was protested by far-right students. Their rhetoric brought to mind some of the darkest moments of 20th-century history – and overlapped with mainstream Israeli views to a shocking degree. By Omer Bartov

This week, we’re picking some of our favourite pieces from the last few months just in case you missed them…Zoe Williams turns the tables on veteran interviewer Louis Theroux; how an app sparked a late-life gender transition for author Lucy Sante; and if you kill someone in your sleep, are you a murderer?

As he announces ‘understated’ fourth album Small Changes, the Mercury-winning musician explains how he went from ‘slight weirdo’ to wowing Glasto – and why more of us are turning to religion

When people see my physique, abs and mental state, no one can believe my age

Revelations over ex-BBC presenter sent shockwaves across corporation and exposed industry-wide power imbalances

New wave of Formula One fans inspired by Netflix series Drive to Survive say it is time for an African country to host a race

The US supreme court justice accepted $900 concert tickets from billionaire Gloria von Thurn und Taxis. Who is the socialite linked to rightwing networks?

We wanted to understand First Nations stories of first contact with the British explorer rarely told in history books, and so we asked

Conference in the Albanian capital aims to agree how women want the international community to react to the Taliban’s assault on their rights – and fight the erasure of their voices

Research suggesting certain species can learn, experience pain and form relationships has implications for our attitude to world’s most-eaten animal

Drone operators and a volunteer medic on the ever-changing dynamics on the frontline of the Ukraine incursion