Every sentence in this lesson puts the noun in the genitive case — showing possession (der Hut des Mannes, "the man's hat"), or after a genitive preposition (wegen, trotz, während, statt, innerhalb, außerhalb, aufgrund — "because of/despite/during/instead of/within/outside of/due to"). The definite article changes depending on the noun's gender:

Masculine and neuter share the same genitive article, des — only the feminine article changes, to der (the same form it takes in the dative). Masculine and neuter nouns also add -s or -es to the noun itself in the genitive (Mann → Mannes, Kind → Kindes) — feminine nouns never change, matching the pattern in indefinite-articles-genitive.json.