Do the terrorists misunderstand Islam or not?

Salah Abdeslam, 32, is standing trial for being one of the group of Muslims who murdered 130 people in Paris on the evening of 13 November 2015. Rejecting the terms "terrorists" and "radicalism", he told the court that theirs was an "authentic Islam". 

I had a close and very erudite Muslim friend (may he rest in peace) who told me many times that the extremists completely misunderstood Islam. 

He drank wine and read the Guardian. 

Was he or Abdeslem right? 

Are there passages in the Koran or hadiths that throw light on this?

Tony Blair and David Cameron said that the Islamists have misunderstood the Koran, but is either a good Koranic scholar?

The Prophet's biographies are too late to be of any real value but they and much better sources, 7th and 8th century Christian writers, make Mahomet/Muhammed and the Righteous Caliphs who came after him sound like Islamists.

The best evidence that they were is not the written sources but the extent of their conquests in the 7th and early 8th centuries, stretching to the Swiss Alps. 

They have held onto most of those conquests until today, though they were expelled from Western and much of Eastern Europe.

Ann Coulter tweeted on 13th November 2015, 'Donald Trump was elected President tonight'. 

Was she right?

That day Mark Steyn penned (well, typed) with Swiftian irony a piece that I recommend you click on, headlined

The Barbarians Are Inside, And There Are No Gates