It is the second high-profile terror trial heard in a Manhattan federal court after Osama bin Laden's son-in-law and former Al-Qaeda spokesman Suleiman Abu Ghaith was convicted on March 26.
Mustafa Kamel Mustafa, better known in Britain as Abu Hamza al-Masri, is blind in one eye and lost both arms, blown off above the elbow, in an explosion in Afghanistan years ago.
As Abu Hamza sat in court, district judge Katherine Forrest briefly explained to potential jurors the 11 charges against a man accused of being a terror facilitator with a global reach.
He is also accused of providing material support to bin Laden's terror network, of wanting to set up a computer lab for the Taliban and sending recruits for terror training in Afghanistan.
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The defendant, who turns 56 tomorrow, will likely face the rest of his life in a maximum security US prison if convicted during what is expected to be a four-week trial.
Jury selection is expected to conclude later on today, but with the court in recess tomorrow and Wednesday, opening arguments are only expected on Thursday.
He was first indicted in the United States in 2004 and served eight years in prison in Britain before losing his last appeal in the European Court of Human Rights against extradition.
Flown to the US in 2012, authorities lost no time removing his trademark prosthetic hook that he wore in the place of one hand.