The Illuminati is a group that the government denies exists. This group originated in the 17 hundreds, and is said to have been destroyed in the same decade. However, there are some people (like me) that do belive that the Illuminati exists. The Illuminati is belived to be the controlling force in the government, having members from the CIA, FBI, NASA and the DOD. The Illuminati's plan is too put Alternative 3 into action. Alternative 3 is a plan for a one world government with these men as the heads of it. The base of the Illuminati is said to be in Pine Gap in Australia. Now whether this group exists or not is still to be found but there have been some actions that give evidence.
Check out these refering websites dealing with the Illuminati. Some of these sites are cool and will give you a better understanding of the Illuminati.