EU, EEA and Switzerland
If you are going to stay in Austria for more than three months you have to register with the competent residence authority (Magistrat, Bezirkshauptmannschaft) within four months of your stay and you will receive a confirmation of registration.
Further information can be found here.
Nationals of third countries
In principle the application for the residence title has to be done at the competent Austrian embassy in the country of residence. Alternatively, the application can be done at the competent residence authority (Magistrat, Bezirkshauptmannschaft) in Austria during the visa-free stay. Further information can be found here.
Renewal of your residence Permit
You have to apply for an extension before the original permit expires. Information can be found here.
You will find the address of the competent residence authority on the website of your Regional Office.