Al Qaeda is an Islamic extremist group behind the September 11th bombings and other atrocities. Al Qaeda is linked to the Wahabi branch of Sunni Islam and other extreme branches. According to Al Qaida anybody including other Muslims who does not support the Al Qaeda Jihad against the United States, Israel and their allies is worthy to be killed. Al Qaeda frequently uses suicide bombings and attacks several targets simultaneously.
Terrorist attacks may involve members of Al Qaeda or may be carried out independently by terrorists trained by Al Qaeda. There are also terrorist acts inspired by Al Qaeda but not involving the organization at all, Al Qaeda likely does more harm by encouraging other Muslims to carry our terrorist outrages and by giving other terrorists philosophical underpinning than through what Al Qaeda does directly. Al Qaeda teaches that killing innocent people is justified during Islamic Jihad.
One of many aims Al Qaeda has is to replace more liberal regimes in Islamic countries with Islamic fundamentalist regimes.