This is a classic Swedish children's book in rhyming couplets with an unusual feature: the rhyming word in the second line of the couplet is (nearly) always omitted, so the child has to guess it himself. It's odd that it hasn't been done more often since then. Let me try and give you the effect in translation:
I'll bet you'll be surprised when you learn that
They lived inside an old, abandoned ...
The missing word, in case it isn't obvious from the cover, is "hat". It's cute.
And the artwork, as always in Elsa Beskow's books, is charming. But... I'm sorry. I'm really doing my best to read it in its historical context, and I don't want to come over all PC, but it's so sexist, ageist and everything-else-ist that I just can't appreciate it properly. Let me tell you the story, and you can judge for yourselves. We have a single mother tomte
(sort of gnome/leprechaun very popular in Swedish mythology) and her three kids, who live in the aforementioned hat on an island. On the shore we have a male tomte who lives in a tree-stump.
One day, the mother rows over to the shore. The kids decide they'll make themselves useful and wash all the clothes. Unfortunately, the fire they start ends up burning their house down, so when Mom gets home there's just smouldering ashes and three terrified children. Things don't look too good! But the male tomte says hey, why don't we get married? You can come and live in my tree-stump, and I'll make sure I beat some sense into those bratty kids of yours. She accepts, and they live happily ever after.