Personnummer is your unique identity number in the form, (YYYYMMDD-XXXX), begins with your date of birth plus 4 unique digits. You can apply to it if your enrolled program is longer than 1 year. It is a must for more or less everything to have a smooth life in Sweden.
Once you are in Sweden, you can go and register at the Swedish Tax Agency – Skatteverket. It is not possible to apply online, you need to be present in person there, can be a bit cumbersome at times. This also applies to your family who is moving with you to Sweden. It might take a a couple of days to few weeks to receive your personnummer by post at your registered address.
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