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

Masculine and neuter share the same genitive article, eines — only the feminine article changes, to einer (the same form it takes in the dative). Masculine and neuter nouns also usually add -s or -es to the noun itself in the genitive (Mann → Mannes, Kind → Kindes) — feminine nouns never change.