Question

Why does Homer invoke the muses

Answer 1

O Muse, of the man of many devices, who wandered full many ways after he had sacked the sacred citadel of Troy. Many were the men whose cities he saw and whose mind he learned, aye, and many the woes he suffered in his heart upon the sea, seeking to win his own life and the return of his comrades. Yet even so he saved not his comrades, though he desired it sore, for through their own blind folly they perished—fools, who devoured the kine of Helios Hyperion; but he took from them the day of their returning. Of these things, goddess, daughter of Zeus, beginning where thou wilt, tell thou even unto us." 

The narrator asks for inspiration to begin telling the tale of Odysseus.