"If Islam Embodies Belief in Peace, Why Do Muslims Kill Other Muslims in Such Great Numbers?"

Good question. I'd answer it like this: if you substitute the word "control" for the word "peace," it all makes sense. Islam is a religion of control--controlling the thoughts and actions of adherents; a Utopian longing for the "peace," i.e. the control, that will be in place once Islam is calling the shots everywhere for all time. And who will be in control then? Well, that's why they keep fighting (which they've done since the death of Islam's founder left a void and sparked a struggle for succession)--to determine who'll be on top.

Update: An adherent named Mahou Shoujo comments:

Read the Qur'an and take it for what it says. Do not try and put western values of concepts on it. Pay careful attention to what the remedy is for any transgression against Islamic law. Note that there is not division between religion and government in Islam.

So noted, M.S.