The 44-year-old, who emailed out copies of a manifesto before his attacks setting out his theories, is also suing the state in a bid to lift restrictions on his correspondence with the outside world.
Breivik killed eight people with a car bomb in Oslo and gunned down 69 others, most of them teenagers, on Utoeya island. He has been held in isolation ever since.
He is scheduled to start testifying at on Tuesday afternoon.
"I want to hear him directly, not via the media," said Freddy Lie, the father of two daughters who were at Utoeya in 2011 - one was shot dead, the other was wounded but survived.
Lie was present at the first day of the legal proceedings on Monday and told Reuters he was planning to attend on Tuesday.
Some journalists had asked Judge Birgitte Kolrud to let them broadcast Breivik's testimony. But she ruled against that last week saying there was a risk his statement could become a platform for his views rather than testimony about his jail conditions.
Breivik's lawyers argue Norway is breaching the European Convention on Human Rights, including sections saying no one should be subject to "torture or to inhuman or degrading treatment or punishment".
His isolation for more than a decade has left him in a "locked world" with only guards and other prison professionals whose duty is to maintain their distance, his lawyer Oeystein Storrvik told the court on Monday.
Lawyers for the Justice Ministry say the curbs are necessary as Breivik remains a threat and could inspire others to commit violence.
On Monday, the court heard the Norwegian police security service, PST, had assessed last year that Breivik continued to be a source of inspiration for far-right extremists worldwide.
The hearing is being held in the gymnasium of the high security Ringerike prison, in a room equipped with a climbing wall and two basketball hoops. The jail is where Breivik is held and is on the shore of Tyrifjorden lake, where Utoeya lies.
The case is scheduled to run until Friday. The judge's verdict will be issued in coming weeks. There is no jury.
