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μή is a negator like οὐ. In broad terms, while οὐ is used in statements and is usually found with the indicative, μή is used in more 'complicated' constructions, like conditionals and purpose clauses and is usually found with non-indicative forms. Here it adds the negative sense 'not'. For example:

τί ἄν οὖν βουλόμενος ἐγὼ τοιοῦτον κίνδυνον ἐκινδύνευον, εἰ μὴ τὸ μέγιστον τῶν ἀδικημάτων ἦ ὑπ’ αὐτοῦ ἠδικημένος;
Lysias Speeches 1.45

ἵνα δὲ μή, ὁπότε λοῦσθαι δέοι, κινδυνεύῃ κατὰ τῆς κλίμακος καταβαίνουσα, ἐγὼ μὲν ἄνω διῃτώμην, αἱ δὲ γυναῖκες κάτω.
Lysias Speeches 1.9

μή can also be used in prohibitions, where it can be translated 'don't'. This is followed by the present imperative or the aorist subjunctive. For example:

μήτε τοίνυν ταῦτα φοβοῦ
Plato Crito 45a

μὴ θαύμαζε τὰ λεγόμενα ἀλλ’ ἀποκρίνου
Plato Crito 50d

μή σε πείσῃ Κρίτων ποιεῖν ἃ λέγει μᾶλλον ἢ ἡμεῖς.
Plato Crito 54d

Remember, μή can be extended in various ways and still be used in prohibitions.
For example:

μηδεμιᾷ πολυπραγμοσύνῃ προσεληλυθέναι με νόμιζε πρὸς σέ
Lysias Speeches 1.15

ψεύσῃ δὲ μηδέν, ἀλλὰ πάντα τἀληθῆ λέγε.
Lysias Speeches 1.18

Thirdly, μή is used with the meaning of the conjunction 'lest', particularly after verbs of fearing.
For example:

οὔτε συνῄδει κακὸν οὐδὲν ὃ ἐγὼ δεδιὼς μή τις πύθηται ἐπεθύμουν αὐτὸν ἀπολέσαι,
Lysias Speeches 1.43

ὡς ἔγωγε καὶ ὑπὲρ σοῦ καὶ ὑπὲρ ἡμῶν τῶν σῶν ἐπιτηδείων αἰσχύνομαι μὴ δόξῃ ἅπαν τὸ πρᾶγμα τὸ περὶ σὲ ἀνανδρίᾳ τινὶ τῇ ἡμετέρᾳ πεπρᾶχθαι
Plato Crito 45e


You should also learn 2 important combinations including μή: ἀρα μή is used to suggest that the result is something that you do not want to happen:

ἆρά γε μὴ ἐμοῦ προμηθῇ καὶ τῶν ἄλλων ἐπιτηδείων μή, ἐὰν σὺ ἐνθένδε ἐξέλθῃς, οἱ συκοφάνται ἡμῖν πράγματα παρέχωσιν ὡς σὲ ἐνθένδε ἐκκλέψασιν, καὶ ἀναγκασθῶμεν ἢ καὶ πᾶσαν τὴν οὐσίαν ἀποβαλεῖν ἢ συχνὰ χρήματα, ἢ καὶ ἄλλο τι πρὸς τούτοις παθεῖν;
Plato Crito 44e

Similarly, ὁπως μή means 'see to it that this does not happen'. For example:

ὅπως τοίνυν ταῦτα μηδεὶς ἀνθρώπων πεύσεται· εἰ δέ μή, οὐδέν σοι κύριον ἔσται τῶν πρὸς ἔμ’ ὡμολογημένων.
Lysias Speeches 1.21

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Further examples of constructions associated with this topic: