The genitive case is also sometimes called the possessive case, and for good reason: it is integral in indicating the possessor (somebody or something that possesses something. I love it when the grammar terminology is clear and easily understood).
The genitive case It is equivalent to the English:
Here, we’re not going to go into how to form the genitive case, just how to use it to indicate possession. If you’d like to learn how to form the genitive of a noun, I recommend Brian Casper’s YouTube channel Icelandic For Foreigners, starting with this video .
Note also that here we’re talking about the genitive case for nouns, not pronouns. You can also indicate possession in Icelandic with various types of pronouns, notably:
What most people get wrong about using a genitive noun is that they think it works just like the genitive pronouns, but that’s not the case. Most notably, the difference is in how we use the definite article (the word the in English).
*I mean, it’s language. Never say never. But it’s still a pretty good rule.
By the by, notice the word order: it’s not the student’s mother, it’s mother the student’s. This works exactly like when the possessor is a pronoun, so it’s standard practice in Icelandic.