Not to be confused with Carthage, the fifth sector on Lyoko.
In the novels, the project is described to create a weapon of mass destruction, which the series specifies as (in Franz Hopper's diary, circa The Key) a system designed to "disrupt enemy communications." However it was made to do this, Franz Hopper said that the project was far too dangerous for use, and that he desires to destroy it. Whether or not he ever succeeded is unknown.
In the Seasons 2-4 end credits, some information about the project is revealed in the form of various photographs from a dossier about Waldo Schaeffer, with one particular photograph showing that there were many scientists involved in the project and that, while Franz Hopper was young during the project's (presumably) early years, Anthea fell pregnant with Aelita, gave birth to Aelita and sufficient time passed to allow Aelita to grow to the age of 12 (by 1994).
Waldo and Anthea defected from the project for ethical reasons. The Men in Black later kidnapped Anthea from the Mountain Cabin because of this. Aelita and Franz went into hiding because of this, with Waldo changing his name from Waldo Schaeffer to Franz Hopper. He consequently created the Supercomputer, Lyoko, X.A.N.A., and the return to the past program to destroy the project. Lyoko's fifth sector was code-named Carthage after the project.
After this, the Men in Black found them, again, and Franz and Aelita fled to Lyoko to escape the Men In Black. There, X.A.N.A. imprisoned both and used the information contained in Carthage to try and destroy humanity.
Current Events (Seasons 2-4 and Evolution)
In the present day of the series, Project Carthage is first mentioned during the events of Franz Hopper, where X.A.N.A. Franz Hopper mentions that Lyoko started out as a program meant to counter a military project that was based on a multi-agent system. This detail is confirmed in The Key, where Franz Hopper reveals in his diary that Lyoko and X.A.N.A. were indeed programs written to counter a military project, identifying it as Project Carthage.
However, following these two episodes, Project Carthage is not mentioned directly again. Only at two points in the series are any events shown that are directly linked to Carthage. Aelita reveals how X.A.N.A. rebelled against Franz, while Distant Memory shows Anthea's kidnapping by the Men in Black, who are assumed to be related to the project. Beyond these episodes however, Project Carthage is never mentioned, or shown again, and ultimately does not factor in the Lyoko Warriors' quest to stop X.A.N.A...
During Season 5, the Lyoko Warriors, trying to figure out the mystery of X.A.N.A.'s return, discover a virtual world known as the Cortex, run by Professor Tyron, who, at least according to a piece of archived security footage, used to work with Hopper, but whether or not it was during, before, or after Project Carthage is never confirmed. However, it is confirmed that Tyron's base of operations is located in Switzerland, a country that is believed to have been one of the main locations of research related to Carthage, and that Anthea is working with him for reasons unknown. Tyron later states to Aelita that one of his goals is to retrieve Hopper's archives, but whether or not this relates to Hopper's diary or other pieces of work is unknown. In the end, while it is certain that Tyron plays a more direct role concerning Project Carthage, the season ends without any solid confirmation of what that role is, and the Project fades away into the background once more.
Chronicles (Alternate Continuity)
In the alternate continuity of the novels however, the forces behind Project Carthage are finally revealed and take center stage. Originally, Project Carthage started out as a humanitarian project meant to revolutionize communication systems, holding at its core a virtual world known as the First City, which had a futuristic and medieval blend in its theme. However, the First City had a "dark zone" secretly installed that would work as an override to turn the project into the system that Hopper described in his diary, a system that could override all forms of communication across the globe and put them under the control of whomever activated this dark zone. Waldo and Anthea discovered this in time and took their work elsewhere, abandoning the project and leaving it incomplete. It is unknown who slipped the coding for this override into the First City.
Afterwards, the events described in the background details section took place, with the mastermind behind Anthea's kidnapping revealed to be one Mark Hollenback, who later took on the identity of Hannibal Mago, holding Anthea ransom in order to force Waldo to return to the project. It is later revealed that ultimately, Carthage proved to be too uncontrollable in its current form, with many of its backers abandoning the project, especially with the end of the Cold War. The Men in Black from the United States then led the charge in utilizing the technology created during the project's research to erase the memories of everyone related to it.
This however, extended to Lyoko, which was revealed to have been created from Carthage's old templates. However, the "dark zone" that had been placed in it could not be removed, prompting Hopper to program the surface sectors and Carthage as a firewall in the virtual world in order to keep this zone inaccessible, as well as to create Code: DOWN, a self-destruction code that would delete the supercomputer's data, rendering the hardware inoperable and destroying the virtual world for good.
In the end, under threats from the Men In Black, Hopper had his research team's memories erased, and utilized a piece of technology known as the "Memory-Snatching Glove" to implant his backup data into Aelita's brain before making his escape.
Throughout the novels, the forces concerning Carthage are revealed to come from the U.S. Men In Black (Which, while not named, are likely the CIA), who seek to destroy all of the technology and data from Carthage, and the Green Pheonix, a mafia-like terrorist organization who benefited from the technology that Carthage created, having previously been the main benefactors to the research concerning Lyoko, albeit without Hopper's knowledge.
Ultimately, after much trial and tribulation through discovering these secrets, the Lyoko Warriors, with the help of a reformed X.A.N.A. and new ally Eva Skinner, manage to stop the Green Pheonix from turning Lyoko's systems into a weapon, and utilize the Code: DOWN to render Lyoko inoperable, preventing its data from being utilized again and ending the threat that Carthage posed to the world.
It should be noted that much of what is discussed in this section is heavily summarized in several areas, and belongs to an alternate continuity, holding details that seem to contradict what was shown in the main series. However, beyond the altered details, what is revealed seems to fit snugly into the show's unknown backstory, putting many unknown events into detail. Regardless, whether or not these details are truly 'canon' is unknown, as an interview with Sophie Decroisette reveals that while the writers of the novels had the original concept documents as a starting point, they may have diverged from what she had written, though due to not reading the novels, she could not confirm this last detail.