One student was shot in the chest and seriously wounded and two men were shot outside the building and suffered lighter injuries, police and Health Ministry officials said.
The gunman left a note accusing his fellow students of picking on him, and posted the message on a social networking site.
"I have now reason to continue living. But, unluckily for you, I'm too selfish to leave and let you keep living ... ," he said in the note which was written in Greek.
"For me, you are all garbage. ...Whoever I see on the morning of April 10 will immediately become a target," he wrote, adding that he had been "rejected" by someone he had fallen in love with. "Until now, I have received nothing but rejection and contempt from those around me."
Police confirm the man seen on the posting on the site was the 19-year-old gunman, whom they identified as Dimitris Patmanidis. Included in the posting - put up about three hours before the attack - are 17 photographs, several of which show the man pointing a gun at the camera.
Police said Patmanidis was an immigrant from the Georgian breakaway region of Abkhazia. He entered the college carrying two handguns, a knife and 66 9mm bullets, according to police and college administrators.
The youth had apparently planned to take more lives, police said, because he was carrying two guns and because of the language used in the Internet posting.
According to the police account, the gunman arrived around 8:45 a.m., a quarter of an hour after lessons had started at the OAED state unemployment agency's training college in the Athens Rendi district.
He shot the student victim on a college stairwell leading to the second floor before running out. He then shot two workers at a nearby shop who tried to stop him, one in the leg and the other in the arm. Then he went to a park close to the school and shot himself in the head, police said.
Fellow students and college staff described the gunman as a loner who favored black clothing and long overcoats.
"He was generally very well behaved. Teachers told me he did not socialize with the other kids," said college director Apostolos Pyrgolios, who witnessed part of the shooting.
"I heard a popping noise. I thought it was firecrackers and went to see what was happening. I Saw Dimitris. He had a gun pointed at me and told me to get out the way. Then he run out the building."
The Health Ministry said the injured student suffered gunshot wounds to the chest, arms and legs, while the other two men had lighter injuries. They were identified by police as a 23-year-old Greek and a 47-year-old Albanian.
Police spokesman Panayiotis Stathis told The Associated Press that the gunman shot his 18-year-old fellow student four times.
"It seems his motive was revenge," Stathis said.
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