You may already know the Swedish holiday greetings god jul! (Merry Christmas!) and gott nytt år! (Happy New Year!), but there's a third seasonal saying that comes in particularly handy during the mellandagar and onwards.
God fortsättning literally means 'Happy continuation', and can generally be used from Boxing Day to early January. Used between Boxing Day and December 31st, it means 'have a good rest of the holiday season!', which is a bit of a mouthful in English, and from January 1st onwards it is used to mean 'have a good rest of the year!'. On December 30th and 31st, you can also use gott slut! (Happy end of the year!)
Whereas English-speakers tend to say 'Happy new year' to friends they see in the first days of January, if it's their first meeting since before New Year's Eve, Swedish god nytt år is usually used only immediately after the clock strikes midnight on January 31st, so god fortsättning is the more common early January greeting.
It's a useful little phrase, but how long can you keep saying it before it sounds a bit strange? This is a question that confuses even native Swedish speakers.
In general, you're safe wishing friends a god fortsättning at least up until Epiphany (January 6th), and can probably carry on using it until the 20th day of Swedish Christmas, tjugondag knut, on January 13th, when the seasonal decorations are generally taken down. After that, it's time to revert to the usual greetings such as god helg (have a good weekend), god morgon/god kväll (good morning/good evening).
God fortsättning can also be used after other significant events, particularly Midsummer, which is just as important in the Swedish calendar as Christmas. So if you see friends shortly after the Midsummer weekend, you could wish them a god fortsättning meaning 'enjoy the rest of summer'.
God fortsättning på det nya året
Happy continuation of the new year (a longer form of the greeting)
Jag ville önska god fortsättning till din familj
I wanted to wish your family a happy rest of the year