AQI was a cell of al Qaeda that focused itself in Iraq
It frequently went back and forth between Syria (where it got supplies) and Iraq (where it was fighting)
Many of its members were sent to Camp Bucca and were able to meet up with other radicals, and form the plan of establishing ISIS
When the Syrian civil war broke out, AQI saw a opportunity and moved into Syria, merging with the cell there, in direct violation of order from al Qaeda HQ
After a small mini-war between the two groups, they formally separated and went their own ways
The list of crimes committed by ISIS is a very long list
Just some of the major things they have done include: terrorist attacks on other countries, the genocidal massacre of people they deem "unfit", racketeering, extortion, rape, murder, trafficking, and many other unspeakable acts