Anti-migrant, anti-Muslim, anti-Merkel
The AfD is dominated by white men, is strongest in Germany's poorer ex-communist east, and has flirted with far-right groups, breaking a taboo in post-Holocaust Germany.
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Close to France's National Front and the UK Independence Party, the AfD is an anti-establishment party that harnesses xenophobia and popular discontent about what it labels unaccountable political and media elites.
Its leaders have sparked outrage by saying German border guards should as a last resort open fire on illegal immigrants, calling Berlin's Holocaust memorial a "monument of shame" and suggesting a Turkish-born German politician be "disposed of in Anatolia".
The AfD is shunned as a radical fringe group by all mainstream parties, but its rise further fragments the political landscape and will complicate coalition-building efforts by the likely election winner, Chancellor Angela Merkel.
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How did it start?
The AfD was founded during the eurozone debt crisis in April 2013 when it labelled the single currency "a historic mistake" and campaigned against bailouts for crisis-hit southern economies.
It narrowly missed the five-percent hurdle for entry into parliament in elections four years ago but then notched up wins in several regional votes and, in 2014, won seven seats in the European Parliament.
The right-winger Frauke Petry in 2015 toppled the AfD's founder, economics professor Bernd Lucke, who quit the party.
The mass influx to Germany of mostly Muslim refugees and migrants in mid-2015 revived the AfD's flagging fortunes as it angrily attacked Merkel's open-door policy.
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Like the far-right PEGIDA protest movement, the AfD accused her of "treason" and linked her immigration policies to jihadist attacks in Europe and sexual attacks by North African migrants in Cologne on New Year's Eve 2015-16.
After a series of regional election wins, it now sits on the opposition benches of 13 of Germany's 16 state assemblies.
What does it want ?
The AfD holds that "Islam does not belong to Germany," a country with 4.5 million Muslims, and campaigns with slogans such as "bikinis not burkas".
It wants more law and order and promotes traditional, conservative "family values", urging ethnic German women to have more babies.
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The AfD demands the rolling back of European integration and promotes pro-market economic policies, putting it at odds with the anti-globalisation National Front of France.
It disputes man-made climate change and has called the VW diesel emissions scandal a "witchhunt".
The party wants to "return power to citizens", including through Swiss-style referendums.
In foreign policy, like some other European protest parties, it advocates closer ties with Russia.
Where is it headed?
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Poll support has dropped back from a peak of 16 percent at the height of the migrant influx to 8-12 percent now.
"The refugee issue has lost some of its immediacy," said political scientist Hans Virchow, adding that many voters had also been turned off by inflammatory comments on German wartime guilt by far-right AfD member Bjoern Hoecke.
After new bouts of party infighting, members voted against making Petry their top election candidate, and the AfD entered the race with an unlikely duo.
One top candidate is Alice Weidel, 38, a Goldman Sachs economist who with her partner, a Sri Lankan-born woman, has adopted two children.
The other is Alexander Gauland, 76, who has repeatedly sparked outrage with racist comments, once claiming that Germans would "not want as a neighbour" a football star with a Ghana-born father.
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He also recently questioned Germany's obligation to atone for its Nazi past.
At the international level, the AfD has established contacts with France's Marine Le Pen, UKIP and Dutch anti-Islam politician Geert Wilders, while voicing support for US President Donald Trump -- a stance that could become a liability.
For now the Trump election and Brexit have "acted as a vaccine against the seemingly unstoppable rise of far-right populism in Europe," argued Joerg Forbrig from the German Marshall Fund.
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