According to claims submitted to the court, the 37-year-old alleges his treatment breaches Article 3 of the convention, prohibiting "inhuman or degrading treatment," and Article 8, which guarantees respect for "private life" and correspondence.
The state's legal team argues the restrictions on the killer are appropriate and proportionate, given the seriousness of his crimes.
Breivik was sentenced to 21 years in prison in 2012
-- the maximum possible sentence under Norwegian law, but one which could be extended if he is considered to still pose a threat to society.
Due to security considerations, proceedings in the suit are being heard inside a gymnasium at Skien prison, which has been temporarily converted into a courtroom.
Appearing in public for the first time since his trial, Breivik, dressed in a black suit and gold tie, appeared thinner than he had previously, and sported a closely shaved head. He made the Nazi salute after his handcuffs were removed on entering the courtroom.
At the end of the day's proceedings, Judge Helen Andenaes Sekulic instructed Breivik not to repeat the gesture when he returns to court to testify on Wednesday.
Breivik's case centers on the complaint that he is banned from contact with other inmates, has limited contact with prison guards and had had virtually no contact with anyone outside a professional capacity.
It claims his only visitor in a non-professional context has been his mother, before her death in 2013, and that during her visits, they only had about five minutes together when they could hug. His only other visitors were restricted to communicating with him through a glass panel.
His complaint claimed the approval process for visits was so strict that it effectively prevented visits, as were the restrictions on his mail, which denied him the opportunity to build relationships.
It also complained that he had been subjected to more than 800 nude inspections, some of which were carried out by female prison officers, and none of which had found anything.
State: Restrictions proportionate
In response, the state legal team argued in papers submitted to the court that the high security restrictions placed on Breivik were appropriate given the seriousness of his crimes, and well within the limits allowed for under the European Convention on Human Rights.
It argued that Breivik was a very dangerous man -- a mass killer who was methodical, rational, and who had shown no regret for his actions.
The documents argued that restrictions, such as the time spent in handcuffs, had been gradually eased in line with ongoing risk assessments.
The defense documents claimed Breivik received regular visits from a "visit friend" and priest, and that he undertook correspondence studies with the assistance of a social worker.
Breivik had access to a computer, without Internet access, as well as writing tools, a TV and a PlayStation gaming console, the documents said.
They claimed that censorship of his mail was not in breach of the European Convention on Human Rights, and was appropriate given the risk that he would contact far-right sympathizers and potentially encourage them to commit acts of violence or terrorism.
It only takes one Breivik to inspire another, state lawyer Adele Matheson Mestad told the court Tuesday.
Letters, phone calls to sympathizers
Mestad said that out of a total of 4,000 letters sent to or by Breivik, about 600 had been blocked by prison authorities. These were letters attempting to establish networks or encourage extremism, both in Norway and abroad, in countries including the United States, Britain, Russia and Poland, Mestad told the court.
The biggest category of correspondence blocked were mass letters to supporters -- people he didn't know personally, but with whom he was attempting to build networks due to their shared racist ideology.
Another category of blocked mail was sent to prison inmates, attempting to establish "brotherhoods" in prisons.
In Breivik's 1,500 page anti-Islam, anti-liberal political manifesto, called "2083: A European Declaration of Independence," he wrote that prisons were an ideal venue to recruit followers to his political cause -- all the more reason to be legitimately concerned about his networking efforts, the state's legal team claimed.
Letters to Breivik from sympathizers were also blocked, Mestad said.
Breivik also had three active "fans" who had sought to visit him, but who had been prevented by prison authorities, she said.
One had had telephone contact with Breivik for a period, before prison officers brought a halt to the calls when it was discovered she was sharing the contents of their conversations on a blog.
Survivors look on
Breivik's killing spree on July 22, 2011, was the deadliest attack in Norway since World War II. Eight people were killed when a bomb he planted detonated in Oslo, before he methodically shot to death 69 young people, many of them teenagers, at a Labor Party youth camp on nearby Utoya island.
Breivik blamed the left-leaning Labor Party for the rise of multiculturalism in Norway.
One of the survivors of his shooting spree on the island, Eivind Rindal, told Norwegian public broadcaster NRK that he believed there was good reason to isolate the mass killer in jail, and that he feared Breivik could inspire other extremists to future acts of violence.
Another Utoya survivor, Viljar Hanssen, tweeted Monday that Breivik had "achieved exactly what he wanted" through pursuing the lawsuit, gaining further attention which helped him to spread hate from his cell.
He then tweeted that he was proud and happy to live in a country with a robust system of law that applied to all.