A terraforming experiment of Dr. Carol Marcus.
The Genesis Project was a Federation research effort led by Dr. Carol Marcus and her son, Dr. David Marcus. Its goal was a device that would reorganise matter on a lifeless planet to create a living world, but anyone could see that the same device would destroy all existing life on a world where it was used.
The team worked on the space station Regula One and inside the Regula planetoid. In Star Trek II: The Wrath of Khan, Khan seized the Reliant, raided the station and stole the device. In the final battle in the Mutara Nebula, the dying Khan triggered it, and the Genesis wave formed a new planet from the nebula's matter. Spock died saving the Enterprise from the blast.
In Star Trek III, it emerged that David had used unstable protomatter in the device, which made the new planet age and break apart rapidly. The Klingon commander Kruge tried to seize the secret of Genesis, killing David, and Kirk destroyed the Enterprise to defeat him. The Federation declared the Genesis planet off limits, and the project became a source of bitter controversy.