Fritzl pleaded guilty Monday to incest, rape and sequestration but denied the most serious charges of murder and enslavement.
During opening statements, the prosecution said Fritzl had used his daughter Elisabeth, 42, "as a toy" during nearly a quarter of a century of sexual abuse in a narrow cellar that resulted in seven children.
Fritzl's lawyer meanwhile sought to paint his client as something other than a monster, arguing that he had only wanted a second family to the one he had with his wife Rosemarie, 69.
The prosecution accuses Fritzl of murder for letting a baby die shortly after birth in 1996, according to the 27-page charge sheet.
This charge, which carries a life sentence, is a contentious one as Fritzl says the baby was stillborn and burnt the body.
Fritzl also rejected on Monday the charge of enslavement, which has been brought for the first time in Austria, and denied that he threatened to kill his prisoners last year.
Three children spent their entire lives in the damp cellar with their mother, while another three were brought to live with Fritzl and his wife.
Fritzl however pleaded guilty to incest, rape, sequestration and coercion.
The incest trial of the century has attracted hundreds of journalists from around the world to the small town of Sankt Poelten, some 60 kilometres (37 miles) from Amstetten, where Fritzl held his daughter captive.
No information was seeping out about the content of the testimonies however, as the trial was being held behind closed doors to protect the privacy of the victims.
Each day's session was to begin at 9:00 am (0800 GMT) and go until 4:00 pm.
The verdict was expected by Friday but could come a day early if the proceedings move quickly, the court said.
Erich Huber-Guensthofer, deputy director of Sankt Poelten prison where Fritzl is being held, told journalists Monday: "He is not an exceptional person, if he stood here you probably wouldn't notice him... he's very courteous."
Fritzl's lawyer meanwhile insisted that his client cared for his captives.
"If you only lock up your daughter to have sex with her, you're not going to have any children, you're not going to get schoolbooks (for them) or a Christmas tree."
Prosecutor Christiane Burkheiser however described Fritzl's crimes as "inconceivable", noting that he raped his daughter in front of her own children.
He "showed no sign of regret or any consciousness of wrongdoing," she said.
"He came (to the cellar). Lights out. Rape. Lights on."
The dungeon, which had no heating, hot water, fresh air or sunlight and was hidden behind eight doors, including three with electronic locks, was also damp and mouldy, added Burkheiser.
"I went down there twice and there's a morbid atmosphere."
Four experts, including one who must help determine whether Fritzl let the baby die, and another who will testify about the electronic locks on the doors to the cellar, might be called later in the week.
Elisabeth Fritzl's six surviving children, her siblings and her mother Rosemarie, who maintains she never knew of her husband's actions, have declined to testify, as permitted under Austrian legislation.
Image from Conger, http://geoconger.files.wordpress.com.