Sense

1. used to strengthen statements: surely, truly, definitely
2. (after other particles), (ἦ μήν) absolutely
3. (καὶ μήν) used to introduce something new or convey affirmation
4. (αλλὰ μήν) yet truly, on the other hand
5. (οὐ μήν) certainly not
6. (μήτε μήν) not even

Examples

• ἦ μὴν εὐλογῶν εὐλογήσω σε, καὶ πληθύνων πληθυνῶ τὸ σπέρμα σου, ὡς τοὺς ἀστέρας τοῦ οὐρανοῦ καὶ ὡς τὴν ἄμμον τὴν παρὰ τὸ χεῖλος τῆς θαλάσσης, καὶ κληρονομήσει τὸ σπέρμα σου τὰς πόλεις τῶν ὑπεναντίων. (Septuagint, Liber Genesis 22:17)
• ἀποστείλατε ἐξ ὑμῶν ἕνα καὶ λάβετε τὸν ἀδελφὸν ὑμῶν, ὑμεῖς δὲ ἀπάχθητε ἕως τοῦ φανερὰ γενέσθαι τὰ ρήματα ὑμῶν, εἰ ἀληθεύετε ἢ οὔ. εἰ δὲ μή, νὴ τὴν ὑγίειαν Φαραώ, ἦ μὴν κατάσκοποί ἐστε. (Septuagint, Liber Genesis 42:16)
• ὁ μὴν οὗτος ὑμῖν ἀρχὴ μηνῶν, πρῶτός ἐστιν ὑμῖν ἐν τοῖς μησὶ τοῦ ἐνιαυτοῦ. (Septuagint, Liber Exodus 12:2)
• ἐὰν δὲ μὴ εὑρεθῇ ὁ κλέψας, προσελεύσεται ὁ κύριος τῆς οἰκίας ἐνώπιον τοῦ Θεοῦ καὶ ὀμεῖται ἦ μὴν μὴ αὐτὸν πεπονηρεῦσθαι ἐφ᾿ ὅλης τῆς παρακαταθήκης τοῦ πλησίον. (Septuagint, Liber Exodus 22:8)
• ὅρκος ἔσται τοῦ Θεοῦ ἀνὰ μέσον ἀμφοτέρων, ἦ μὴν μὴ αὐτὸν πεπονηρεῦσθαι καθόλου τῆς παρακαταθήκης τοῦ πλησίον. καὶ οὕτως προσδέξεται ὁ κύριος αὐτοῦ, καὶ οὐκ ἀποτίσει. (Septuagint, Liber Exodus 22:11)

Source: Ancient Greek entries from Wiktionary