If you are an EU citizen moving to Sweden, applying for the right to stay is very simple.

When entering Sweden all you need is a valid form of ID and something to prove you are a resident of an EU country.

As a citizen of another EU country you have the right to work immediately after arriving in Sweden.

However, you must register your existence within the Swedish population with the Swedish Tax Agency and apply for a Swedish ID number which will unlock a number of essential services such as healthcare and education.

[links to swedish tax agency]