The nationalist Alternative for Germany (AfD) has grown rapidly since it was formed in 2013 and is now the biggest opposition party in the Bundestag (national parliament), with 89 seats.
Founded in 2013 as an anti-euro party, it has shifted its focus to immigration and Islam and is increasingly seen as far-right in tone.
Is it far-right?
Yes. It may not have started out as a far-right party but it soon embraced far-right policies and many of its leaders have espoused far-right rhetoric.
AfD co-chairman Alexander Alexander Gauland has talked of fighting an "invasion of foreigners" and the party openly focuses on Islam and migration, seeing Islam as alien to German society. Some of the party's rhetoric has been tinged with Nazi overtones.
The AfD sits in the same political family as France's far-right National Front and Austria's far-right Freedom Party - as well as the populist, anti-Islam Dutch Freedom Party (PVV) of Geert Wilders. Nigel Farage, former leader of the UK's anti-EU party Ukip, took part in their 2017 election campaign.
The party's leader in the eastern state of Thuringia, Björn Höcke, once described Berlin's Holocaust memorial as a "monument of shame" and called for a "180-degree turnaround" in Germany's handling of its Nazi past. Picking up the same theme, Alexander Gauland trivialised the Nazi era as "just a speck of bird's muck in more than 1,000 years of successful Germany history".
The AfD has managed to attract voters from the centre right and even the centre left but in the words of Verena Hartmann, a moderate MP who left the party in January 2020 because it was becoming to extreme: "Those who resist this extreme right-wing movement are mercilessly pushed out of the party."
In the words of Matthias Quent, a German expert on the far right based in Thuringia: "Not everyone in the AfD is ideologically far right, but anyone in the party or even voting for the party is supporting a party that has a far-right objective."
Who to watch
The AfD has only existed for seven years and its leadership has gone through regular, turbulent changes. Its best-known figures are co-leader Alexander Gauland, parliament group leader Alice Weidel and Björn Höcke, the party's most significant figure in its eastern heartland.
Alice Weidel is a 41-year-old economist who divides her time between Berlin and Switzerland, where she lives with a woman adopted as a child from Sri Lanka and their two children.
She is one of a small number of women in prominent positions in the AfD and argues that her presence as one of its top candidates proves the party is not homophobic.
Alexander Gauland, a 78-year old lawyer, has been with AfD from its Eurosceptic start and his political career began decades earlier with the centre right.
As AfD moved to the right so did he, making a number of remarks condemned as racist. In 2016 he talked about footballer Jérôme Boateng, who was born in Berlin to a Ghanaian father. "[Germans] like him as a football player. But they don't want to have a Boateng as their neighbour."
Björn Höcke, AfD's party leader in the eastern state of Thuringia, has been behind some of its biggest controversies. He is also seen as an inspiration to many of the MPs elected to the Bundestag in 2017 and heads a stridently nationalist group called Flügel. He helped AfD in Thuringia push the centre right into third place in state elections in October 2019.
When he criticised the idea of a Holocaust memorial in the heart of German capital, the party moved to expel him but apparently changed its mind.
Mr Höcke helped trigger a national crisis in February 2020 by helping a liberal candidate become state premier in Thuringia. Not since World War Two had the far right played kingmaker in German politics.
Jörg Meuthen, co-leader of the party with Alexander Gauland, is seen as a relative moderate. After the election result he insisted the AfD did not accept racism or xenophobia, but in the same breath complained that "in some German cities, I struggle to find Germans on the streets".
Fighting mass immigration
The AfD's big success came in challenging Angela Merkel's decision to let in around 1.3 million undocumented migrants and refugees, mainly from the Middle East, from 2015.
They tapped into anxieties over the influence of Islam, calling for a commission to investigate the chancellor's "breaches of the law" in allowing them in.
The party made the influx the focus of its party platform. There were contacts with the anti-immigration Pegida movement, which staged weekly marches against what it called "the Islamisation of the West".
Pegida took hold mainly in eastern cities such as Dresden, and it is in the ex-communist east that the AfD has had its biggest successes, attracting more men than any other party. Odd perhaps, in that the biggest concentrations of immigrants are not in those areas.
AfD adopted some of Pegida's anti-establishment rhetoric, such as the slogan "Lügenpresse" ("lying press"), which was used by the Nazis.
Germany must reintroduce permanent border controls and the EU's external borders must be "completely shut", the AfD says. That position contradicts Schengen - the EU's free movement zone, covering most of Europe, where border checks are generally minimal.
One of its former leaders, Frauke Petry, once said German police should "if necessary" shoot at migrants seeking to enter the country illegally. And she was seen as an AfD moderate.
Challenging Islam as 'not German'
AfD adopted an explicitly anti-Islam policy in May 2016 and its 2017 election manifesto had a section on why "Islam does not belong to Germany". "Burkas? We like bikinis," read one of its most garish posters.
The party would ban foreign funding of mosques in Germany, ban the burka (full-body veil) and the Muslim call to prayer, and put all imams through a state vetting procedure.
"Moderate" Muslims who accepted integration were "valued members of society", its argued, while suggesting that multiculturalism did not work.
An estimated three million people of Turkish origin live in Germany, most of them Muslims.
Using nationalist rhetoric
AfD has also built its success on challenging taboos and flirting with racism.
Alexander Gauland drew criticism for declaring that Germans should be "proud" of their soldiers in both world wars. While SS units were notorious for German atrocities in World War Two, the regular armed forces also committed many war crimes.
Frauke Petry once tried to end the taboo on the Nazi-era term völkisch, which comes from the German word for people but was hijacked by the Nazis to define those they saw as belonging to the German race.
Against the euro
AfD has come a long way since it was launched in early 2013 to challenge eurozone bailouts in Greece and elsewhere, and reject the EU's arguments for keeping the euro.
It still promises to abandon the euro and reintroduce the Deutschmark.
But its first leader, Bernd Lucke, left the party in 2015, arguing that it was becoming increasingly xenophobic.
Its anti-euro policy echoes the Euroscepticism of other populist parties in Europe.
If the EU fails to reform and continues centralising, the AfD says, the party will seek to pull Germany out of the EU.