The adjective galen means 'mad' or 'crazy'.
It is used in many of the same ways as English 'crazy'. It's an offensive way of describing someone who is mentally unwell, and should be avoided in this context today. But it can describe an unusual and unwise behaviour or decision (for example: jobba på helgen? Är du galen? – Work at the weekend? Are you crazy?), or to talk about something which is unexpected, unusual or inexplicable. For example: Det här är galna siffror (these are crazy figures) or det är en galen historia (it's a crazy story).
Occasionally, galen means 'wrong' or 'mistaken', and you'll most often see it in this context in the idiom hoppa i galen tunna (literally 'to jump in the crazy barrel/tub'), which in English you could translate as 'to make a fatal error/a huge mistake'. The expression has been around for at least 200 years, and has been linked to an old tale of someone trying to get into a bathtub after a sauna, but accidentally leaping into one full of sticky tar.
The related noun galning (madman/crazy person) is an offensive term for someone with apparent mental health problems, but you might use it affectionately or with awe about someone you know well whose behaviour isn't always understandable: du är helt galen (you're completely crazy). If galen is used with the adjective bli (to become), such as då blev hon galen (then she went crazy), it usually refers to anger.
You can also combine galen with the preposition i to say that someone is 'crazy about' someone or something else, in the sense of being infatuated, in love, or obsessed: hon är helt galen i honom (she's totally crazy about him) or han är galen i katter (he's crazy about cats).
Adding the preposition på to galen means that something 'drives you crazy' in a negative sense, for example: det är en sak som jag blir riktigt galen på (that's something that really drives me crazy).
Some of our multilingual readers might be wondering if there's any link to the renowned physician Galen, who lived during the second century AD. His name, Γαληνός or Galēnos in Greek comes from a Greek adjective (γαληνός) which means 'calm', quite the opposite of Swedish galen.
Well, the answer is no, but the linguistic history of galen is interesting all the same.
It comes from the verb gala (to crow), which today describes the sound made by birds like roosters, and has existed in the Swedish language for centuries.
In older times, this verb also meant 'to cast a magical spell on someone through song', and so galen came to mean 'bewitched'.
There are relatives to the word galen in the other languages of northern Europe. In Icelandic, the word galdur means 'witchcraft' or 'magic trick', and in the past it specifically referred to magic carried out through song. And the English words 'yell' and 'nightingale' are descended from the verb gala too.
Vi lever i en galen värld
We're living in a crazy world
De flesta tycker att jag är galen
Most people think I'm crazy