Mr Fritzl is alleged in 1984 to have lured his daughter into a cellar with windowless soundproofed chambers beneath their house, to have imprisoned her there and raped her repeatedly over a number of years.
The daughter and three of her seven children fathered by Fritzl were kept captive in the cellar until the case came to light in April last year when one of the children became seriously ill and was taken to hospital.
He is accused of murdering one of the newborn twin boys his daughter gave birth to in 1996, having failed to arrange medical care for the ailing infant.
Some legal experts have said it may be hard to prove the murder charge but the charge of enslavement carries a maximum penalty of 20 years, the BBC's Steve Rosenberg reports from St Poelten.
Court spokesman describes first day
Some of the other charges against him carry a sentence of up to 15 years.
While convicts become eligible for parole having served half their sentence under Austrian law, there are other clauses which could prevent an eligible convict walking free if it is considered he could re-offend, our correspondent notes.
Court spokesman Franz Cutka gave an outline of the first day's proceedings.
"After the public was excluded this morning, there was an interrogation of the accused, and the video recording, with the interview of the daughter was played to him and he was questioned about that," he said.
FRITZL CHARGES AND PLEAS
Murder - not guilty plea
Enslavement - not guilty plea
Deprivation of liberty - guilty plea
Rape - partially guilty plea*
Incest - guilty plea
Coercion - guilty plea
*Understood to mean he is contesting the wording of the charges
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