The genitive case indicates possession, and is often shown in German by adding an apostrophe or an ‘s’ to the end of a noun or proper noun.
Das ist Vaters Buch. (S-genitive) OR
Das ist das Buch meines Vaters. (formal genitive)
In English, however, an apostrophe and/or ‘s’ is needed, for example: Stan’s dog, the cat’s food, Chaz’ car. Often, possession is marked through a dative construction instead:
Das ist das Buch von meinem Vater. (dative)
As with the other three grammatical cases, there are case endings associated with the genitive. Here is a chart with the case endings, which is nearly identical to the definite articles chart:
The definite articles for the genitive are ‘des’ and ‘der,’ and the indefinite articles are ‘eines’ and ‘(k)einer’ (the ‘k’ here is used as a stand-in for the plural form).