12:08 PM PT -- The killer has reportedly been revealed as 24-year-old David Kozak. Kozak allegedly killed his father in the day before making his way to the city and shooting people from a balcony at Charles University Arts facility.

9:17 AM PT -- Reports now state the gunman has left at least 15 dead ... including his father, who was found dead earlier in the day.

An unbelievable scene in Prague, as students find safety on the ledge of a building, after a gunman opened fire inside a university building ... with multiple people reportedly dead.

The terrifying moment unfolded Thursday at Charles University in Jan Palach Square, the oldest and largest university in the Czech Republic. It's currently unclear how things started, but images from the scene show a group of students hanging off the building, trying to get out of the shooter's line of sight.

It appears at one point the gunman did get close to the students, because he was spotted on the roof, too ... with his rifle pointing down at the ground below.

Czech police say 10 people are dead, with dozens of others injured -- cops also say the shooter has been "eliminated." He has yet to be identified.

In the midst of the attack, the school's philosophy department was evacuated ... with several people spotted fleeing the scene. An email sent to staff told faculty, "Don’t go anywhere, if you’re in the offices, lock them and place furniture in front of the door, turn off the lights."