This is the first (and only?) interview ever given to a Western journalist.
https://www.facebook.com/JuergenTodenhoefer/videos/101527236...
Seems pretty clear from many sources that their stated goal is to restore the "caliphate" — an Islamic state under the rule of a community of religious scholars guided by a caliph taken to mean the successor to the Prophet Muhammad For them anyone who doesn't believe in their interpretation of Islam must convert or die.
Meanwhile President Obama has encouraging words for them: “The future must not belong to those who slander the prophet of Islam”. So much for free speech and cartoons.
"What ISIS Really Wants" (The Atlantic, March 2015) [0]:
The Islamic State is no mere collection of psychopaths. It is a religious group with carefully considered beliefs, among them that it is a key agent of the coming apocalypse. Here’s what that means for its strategy—and for how to stop it.
[0] http://www.theatlantic.com/magazine/archive/2015/03/what-isi...
They got power because people in the region thought it was a better idea to give them power than to allow our destabilizing influence to continue. Take away all reasons for why they got support in the first place, and they will be marginalized by the people themselves.