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The shooter, identified by authorities as Myron May (31), was fatally shot in an exchange of gunfire with police near the entrance to Florida State's Strozier Library in the latest of a string of shootings on US campuses.
Authorities said they found journals and videos written by May as part of their investigation.
"Mr. May was in a state of crisis," said Michael DeLeo, chief of Tallahassee Police, at a news conference.
A 2005 graduate of Florida State, May received his law degree from Texas Tech University in 2009 and had moved back to Florida about three weeks ago, DeLeo said.
Authorities have not released the names of the three students who were shot. One was treated at the scene for a graze wound. The other two were hospitalized, one critical and the other in good condition, said a spokeswoman at Tallahassee Memorial HealthCare hospital.
Campus security was increased and classes were canceled on Thursday.
FSU President John Thrasher said efforts were under way to restore normalcy to the campus of about 40,000 students, known nationally for the strength of its football team and academics, with weekend events to continue as scheduled.