A truth and reconciliation commission later found that none of the victims were connected to the 'Shining Path' - a Maoist group that carried out an armed campaign against the government.
The prosecution has called for a 30-year sentence and the payment of more than $33 million in damages.
The 69-year-old denies any involvement in any of the killings.
The trial will take place in the police centre in which Fujimori has been held since being extradited from Chile on September 22.
Sessions are scheduled to take place three times a week, and the entire process could last months.
It is the first time in Peru's history that a former president faces a public trial for crimes committed during his administration.
Families of victims of the political violence that gripped Peru between 1980 and 2000 held a rally in the capital, Lima, on Sunday.
Gisela Ortiz, the sister of one of those killed in the 1992 university incident and the representative of the victims' families, welcomed the trial.
|Fifteen people were killed at a party |
in Lima in 1991 [AFP]
However, she also said there was a risk Fujimori could have any punishment reduced or quashed by a later administration.
"There is a danger that in 2011 [after the next legislative elections] there will be a change in the political scene, with stronger support for Fujimori."
Fujimori, who spent five years in self-exile in Japan after fleeing amid a bribery scandal that forced him from power, and was extradited from Chile in September after a long legal battle.
In later trials, Fujimori will face allegations that he illegally used $15 million in state money to pay Vladimiro Montesinos, his intelligence chief, to resign.
He is also accused of authorised bribes to congressmen and illegal phone taps, and that he secretly bought a TV station for political propaganda with state money.