It was notoriously what was declared by Osama bin Laden after 9/11 — which, you must admit, was an occasion of some effectiveness to draw attention to the main group involved, El Qaeda, who in their turn have frequently declared it as the aim of all their training camps in Pakistan, Yemen, N Nigeria [where the individual the original subject of this thread originated]. I think if you google something like 'El Qaeda, declared aims' you will find what I say well documented.

e.g. "The principal stated aims of al-Qaeda are to drive Americans and American influence out of all Muslim nations, especially Saudi Arabia; destroy Israel; and topple pro-Western dictatorships around the Middle East. Bin Laden has also said that he wishes to unite all Muslims and establish, by force if necessary, an Islamic nation adhering to the rule of the first Caliphs."

You will note the aims postulated by both of us are present in this statement of Osama's which I just found online in an 'Infoplease entry on Al-Qaeda.