You certanly can.
However, the process is relativly strict compared to many states in the US.
As a qualified hunter you can own weapons used for this purpose, I believe most semi-automatic rifles are allowed.
To own a pistol/revolver things are more complicated, you have to be a member of a "pistol club" at least 6 months, and then you can buy firearms of this sort after being cleared by the police.
The laws in this country are designed to keep guns of all sorts off the streets, and relativly rare. We are proud in this country to be one of the last countries to have an unarmed police force, though guns are stored in their vehicles and can be made avaliable after being ordered by the high command.
The shooter in this tragedy had guns aquired through legal license, it seems. Unofficially the weapons used were a 5.56mm Mini-14 and a Glock 17, both with several clips and hundreds of rounds of ammunition.