Can you help me to understand the Al-Qaeda?

I have read about their ideology but it doesn't make sense to me. It seems to have hatred for the crusaders and Jews???? They want to fight a war against people who are not fighting them. They have people in all countries just waiting for the go to bomb and kill because they don't agree with the country they live in yet pay them wages and feed them. Or this what I have read. I am told these people are Muslims so if they do not want contact with the rest of the world and live in peace why is it acceptable for them to take the money given to these Muslim countries. I would like to hear from the other world countries their views about giving money to these killers. Someone make sense of this for me. Thanks