Project Genesis was the code name for a scientific research project. Its goal was to develop a process whereby uninhabitable planets could be made suitable for humanoid life. The Genesis effect involved reducing the target space body to subatomic particles, then reassembling them, according to the pre-programmed Genesis matrix.
The project, led by Dr. Carol Marcus, had advanced to "Stage Two", successfully tested inside a cavern on the Regula I planetoid. The madman Khan Noonien Singh initiated a full-scale Genesis effect on stardate 8130, when he stole the Genesis Device and detonated it inside the Mutara Nebula, forming the Genesis Planet. (Star Trek II: The Wrath of Khan)
Despite the fact that initial tests had shown the promise of the Genesis process, the planet created by Khan's actions proved to be unstable. This was shown to be a function of the highly volatile protomatter that had been incorporated by the project scientists into the Genesis process. (Star Trek III: The Search for Spock)
Dr. Carol Marcus presented a proposal and demonstration of Project Genesis to the United Federation of Planets on stardate 7130.4. The Federation had provided substantial funding, and ancillary support from Starfleet, in the form of the USS Reliant, toward its development. Due to the project's potential destructiveness in the event it were used on an already-inhabited world, the project's existence had been classified as secret.
The starship Reliant was assigned to find a target planet, devoid of life, which would be suitable for the project. The Reliant, captained by Clark Terrell, had conducted several unsuccessful searches before arriving at the Ceti Alpha system. Terrell and first officer Pavel Chekov transported to the surface of Ceti Alpha V to investigate life signs, but they were captured by Khan and implanted with mind-controlling Ceti eels. Reliant was subsequently destroyed in the creation of the Genesis planet.
Starfleet ordered the USS Enterprise to investigate. Outraged, Carol Marcus had transmitted a subspace radio message to Admiral James T. Kirk, asking him to intercede. The Marcus team had received what she deemed to be an unusual communication from the enslaved Terrell and Chekov, indicating what the project scientists considered to be a "militarization" of the project. Kirk briefed Captain Spock and Dr. Leonard McCoy about the project, screening a recorded classified briefing featuring Carol Marcus, and computer-generated simulation imagery of the Genesis effect.
Enterprise confronted the hijacked Reliant (whose crew had been marooned on Ceti Alpha V by Khan) and was severely damaged in its successful attempt to stop Khan from fully exploiting the device and the project. (Star Trek II: The Wrath of Khan)
After the detonation of the Genesis device, the Federation Council ordered Starfleet to squelch information regarding the project. Starfleet Admiral Harry Morrow ordered the Enterprise crew to secrecy and had the crew monitored by Starfleet Intelligence and Federation Security. The Mutara sector was declared off-limits, and Starfleet sent the USS Grissom to investigate the newly-formed planet.
Meanwhile, the Klingon spy Valkris had managed to obtain Kirk's classified briefing of the Genesis project and transmitted it to Commander Kruge. Kruge destroyed Valkris's transport vessel, the freighter Merchantman, after she admitted to Kruge having seen the contents of the briefing.
Understanding Genesis' destructive potential as well as its power to create life from lifelessness, Kruge went to the Genesis planet, and destroyed the Grissom with all aboard. An away team from Grissom, consisting of Lieutenant Saavik and Doctor David Marcus, remained on the surface. Kruge killed Marcus, and Saavik was left as the sole survivor from the Grissom team. The USS Enterprise, having been pirated by Kirk, returned to the planet to find and recover Spock, who had been reincarnated by the Genesis effect. Kirk and crew prevented Kruge from accessing the Genesis project files, destroying the Enterprise in the process, while appropriating Kruge's Bird of Prey to themselves. (Star Trek III: The Search for Spock)
After the Genesis planet destabilized, the Klingon ambassador used Kirk's briefing as to Project Genesis, along with images of the destruction of Enterprise, when he spoke before a session of the Federation Council. The ambassador demanded Kirk's extradition by the Federation to the Klingon Empire, to be punished by the Klingons for the Klingon deaths caused when he ordered the self-destruct of Enterprise. He vilified Project Genesis, characterizing it as a weapon created by the Federation in order to bring about the annihilation of the Klingon people. However, Ambassador Sarek, in a rebuttal also before the Federation Council, added that the Klingon ship had destroyed the Grissom and killed Kirk's son, David, in an illegal attempt to possess the secret of Genesis. (Star Trek IV: The Voyage Home)