Plutarch, Life of Alexander 26.4
“When a small box was brought to him—which seem more valuable than the rest of the possessions and baggage they had taken from Dareios, [Alexander] asked his friends what thing seem especially worthy of being put in it. Although many of them made many suggestions, Alexander said that he would keep the Iliad safe by placing it inside. Not a few of the most credible sources claim this.
If, as the Alexandrians say is true—since they believe Herakleides—Homer was no lazy or unprofitable travel companion…”
Κιβωτίου δέ τινος αὐτῷ προσενεχθέντος, οὗ πολυτελέστερον οὐδὲν ἐφάνη τοῖς τὰ Δαρείου χρήματα καὶ τὰς ἀποσκευὰς παραλαμβάνουσιν, ἠρώτα τοὺς φίλους, ὅ τι δοκοίη μάλιστα τῶν ἀξίων σπουδῆς εἰς αὐτὸ καταθέσθαι. πολλὰ δὲ πολλῶν λεγόντων, αὐτὸς ἔφη τὴν ᾿Ιλιάδα φρουρήσειν ἐνταῦθα καταθέμενος· καὶ ταῦτα μὲνοὐκ ὀλίγοι τῶν ἀξιοπίστων μεμαρτυρήκασιν. εἰ δ’, ὅπερ ᾿Αλεξανδρεῖς λέγουσιν ῾Ηρακλείδῃ (fr. 140 W.) πιστεύοντες, ἀληθές ἐστιν, οὔκουν [οὐκ] ἀργὸς οὐδ’ ἀσύμβολος αὐτῷ συστρατεύειν ἔοικεν ῞Ομηρος.
This passage refers to an earlier moment in the Life. Coincidentally, I also sleep the same way…
“[Alexander] was also naturally a lover of language, a lover of learning, and a lover of reading. Because he believed that the Iliad was a guidebook for military excellence—and called it that too—he took a copy of it which had been edited by Aristotle which they used to refer to as “Iliad-in-a-Box”. He always kept it with his dagger beneath his pillow—as Onêsikritos tells us.
When there were no other books in -and, he sent to Harpalos for some more. Then Harpalus sent him Philistos’ books along with some tragedies of Euripides, Sophokles and Aeschylus and the dithyrambs of Telestes and Philoxenos.”
ἦν δὲ καὶ φύσει φιλόλογος καὶ φιλομαθὴς καὶ φιλαναγνώστης, καὶ τὴν μὲν ᾿Ιλιάδα τῆς πολεμικῆς ἀρετῆς ἐφόδιον καὶ νομίζων καὶ ὀνομάζων, ἔλαβε μὲν ᾿Αριστοτέλους διορθώσαντος ἣν ἐκ τοῦ νάρθηκος καλοῦσιν, εἶχε δ’ ἀεὶ μετὰ τοῦ ἐγχειριδίου κειμένην ὑπὸ τὸ προσκεφάλαιον, ὡς ᾿Ονησίκριτος ἱστόρηκε (FGrH 134 F 38)· τῶν δ’ ἄλλων βιβλίων οὐκ εὐπορῶν ἐν τοῖς ἄνω τόποις, ῞Αρπαλον ἐκέλευσε πέμψαι, κἀκεῖνος ἔπεμψεν αὐτῷ τάς τε Φιλίστου βίβλους καὶ τῶν Εὐριπίδου καὶ Σοφοκλέους καὶ Αἰσχύλου τραγῳδιῶν συχνάς, καὶ Τελέστου καὶ Φιλοξένου διθυράμβους.
Plutarch tells a slightly different story in the Moralia
Plutarch, On the Fortune—or Virtue—of Alexander 327f-328a
“Yes, indeed, the accoutrements he possessed thanks to Aristotle were greater than what he got from Phillip when he went against the Persians. But, while we believe those who claim that Alexander said that the Iliad and the Odyssey went with him as guides on his expedition—since we do think that Homer is sacred—don’t we dismiss anyone who claims that the epics followed him as his solace and distraction from work with sweet leisure when the true guide was the reason he had from philosophy and his ‘baggage’ was his notes on Bravery, Prudence, and greatness of spirit?”
ναί, πλείονας παρ᾿ Ἀριστοτέλους τοῦ καθηγητοῦ ἢ Fπαρὰ Φιλίππου τοῦ πατρὸς ἀφορμὰς ἔχων διέβαινεν ἐπὶ Πέρσας. ἀλλὰ τοῖς μὲν γράφουσιν, ὡς Ἀλέξανδρος ἔφη ποτὲ τὴν Ἰλιάδα καὶ τὴν Ὀδύσσειαν ἀκολουθεῖν αὐτῷ τῆς στρατείας ἐφόδιον, πιστεύομεν, Ὅμηρον σεμνύνοντες· ἂν δέ τις φῇ τὴν Ἰλιάδα καὶ τὴν Ὀδύσσειαν παραμύθιον πόνου καὶ διατριβὴν ἕπεσθαι σχολῆς γλυκείας, ἐφόδιον δ᾿ ἀληθῶς γεγονέναι τὸν ἐκ φιλοσοφίας λόγον καὶ τοὺς περὶ ἀφοβίας καὶ ἀνδρείας ἔτι δὲ σωφροσύνης καὶ μεγαλοψυχίας ὑπομνηματισμούς, καταφρονοῦμεν;