If you are an EU/EEA national, you automatically have the right of residence, which includes the right to work in Sweden without a work and residence permit.
A common visa policy forms an important part of the Schengen Cooperation. This allows persons legally living in the Schengen zone to move and work freely within the zone. You and your family members are entitled to begin working immediately. If, however, you stay longer than three months, you have to register within the Swedish Migration Board by using the form Registration of right of residence, no. 141011.
If you are a national of a country that is not part of the EU, you will need a residence permit. You apply for a certificate of residency at a Swedish Embassy or Consulate before entry to Sweden.
Commuters do not need to register
If you are an EU/EEA state national and are working in Sweden but live in another EU/EEA country to which you return at least once a week, you do not need to register in Sweden.