Based on the free movement of workers within the European Union, EU/EEA and Swiss citizens can work in Austria without a work permit. For more information about the transition period, see: www.migration.gv.at/en/types-of-immigration/ mobility-within-the-eu/
In order to immigrate to Austria, third-country nationals need the Red-White-Red Card (Rot-Weiß-Rot Karte). This card offers qualified workers from non-member countries and their families the chance to stay in Austria and work for a specific employer. The Red-White-Red Card must be applied for at the responsible settlement and immigration authority (district or municipal authority), or at the representative authority abroad (embassy) by the person or the employer in Austria.