Genitive

The genitive case denotes source or origin (this function is also called the ablative), or kind or possession. It is also often used for an object of a preposition.

Examples

Ἡ χάρις τοῦ Κυρίου Ἰησοῦ Χριστοῦ καὶ ἡ ἀγάπη τοῦ Θεοῦ καὶ ἡ κοινωνία τοῦ Ἁγίου Πνεύματος μετὰ πάντων ὑμῶν
May the grace of Jesus Christ and the love of God and the fellowship of the Holy Spirit be with all of you
καὶ χωρὶς αὐτοῦ ἐγένετο οὐδὲ ἕν ὃ γέγονεν
and without him nothing was not anything made that was made

"him" is genitive here because it is the object of the preposition "without".