Having learned Nominativ, Akkusativ, and Dativ, you now reach the fourth and final German case: Genitiv, the case of possession or belonging. It answers the question Wessen? — "whose?" — and roughly corresponds to constructions like "the man's car" or "the car of the man."
At A2 level you'll learn two basic patterns. The first, and easiest, applies to proper names like Peter, Anna, or Maria: here you simply add -s directly to the end of the name, with no separate article and no apostrophe — similar to English possessive -s but without the apostrophe: Peter → Peters Auto (Peter's car), Anna → Annas Buch (Anna's book). The only exception is names that already end in s, z, or x, where you add just an apostrophe (') with no extra s: Thomas → Thomas' Buch.
The second pattern is the more important one, since it's used with ordinary nouns rather than proper names. Here it's not just the noun that changes — the article itself changes according to the noun's gender. With masculine and neuter nouns (der/das), the article becomes des, and at the same time you must add -s or -es to the end of the noun itself — unlike Dativ, where only the article changes and the noun stays the same: der Mann → des Mannes, das Kind → des Kindes. With feminine and plural nouns (die), the article simply becomes der, and the noun itself doesn't change at all: die Frau → der Frau.
Word order often mirrors the possessive-of-phrase order: "the car of the man" becomes das Auto des Mannes in German, with the possessed thing first and the owner second, marked by the changing article rather than a separate word for "of."
A useful practical note: in everyday spoken German, many native speakers avoid Genitiv altogether and replace it with von + Dativ, saying das Auto von Peter instead of Peters Auto. In formal writing and on exams, though, the two patterns above are still preferred.
The most common mistake is forgetting to add -s or -es to the end of a masculine or neuter noun after des, writing the wrong die Farbe des Auto instead of the correct die Farbe des Autos. Remember: with des, the article and the noun both change together — not the article alone.