I finally got around to reading The Looming Tower this weekend, probably the best book about the ideology which fuels Al Qaeda and affiliated radical movements. It's a fabulous tour that covers the fifty-year history since Sayyid Qutb began articulating a call for Sharia law in Egypt, through Ayman al-Zawahiri's generation of Egyptian fundamentalists, and the globalization of the call to jihad.
Of course, the final ideology which emerges through Bin Laden and is indoctrinated into recruits of Al Qaeda and affiliates is not sharia law per se, but the Salafist interpretation of Sharia, which disregards 700 years of adaptation and interpretation by Islamic scholars in a process similar to the Jewish Talmudic disputes. The closest analogy in the American system is judges who argue that only "originalist" arguments are proper. The Salafist tradition is no more violent than the American Conservative legal tradition. However, this is the jumping-off point for Al Qaeda's justification of violence.