Migrationsverket is the Swedish Migration Agency. This is the agency that receives applications from people wishing to come to live, work, study, visit Sweden.
The agency has divided itself into 6 different departments: Coming to Sweden, Staying in Sweden, Becoming a Swedish citizen, Needing Protection, Returning to Sweden and Residence and Support.
Staying in Sweden on a “permanent” basis means for more than 5 years. If you are likely to stay in Sweden for up to 5 years, apply for the permanent residency as a matter of process. It will make applying for your Swedish Citizenship a lot easier in the future.
There are a lot of exceptions to right of residency in Sweden and it can be very confusing. Below are links to more information about each of those exceptions.
If you are a resident of another EU country you can read this for more information.
If you are resident of a non-EU country you can read more information here.
If you have been offered a job in Sweden you can read more information here.
If you are married or your common-law spouse is Swedish you can read more information here.