Lines 1-5
ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ
πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν·
πολλῶν δʼ ἀνθρώπων ἴδεν ἄστεα καὶ νόον ἔγνω,
πολλὰ δʼ ὅ γʼ ἐν πόντῳ πάθεν ἄλγεα ὃν κατὰ θυμόν,
ἀρνύμενος ἥν τε ψυχὴν καὶ νόστον ἑταίρων.
1
ἄνδρα μοι ἔννεπε - ἐνέπω in the 2nd person imperative - "tell of" with the accusative. Merry - "It seems rather to be compounded of ἐν and ἔπω, ie. βέπω, and the second ν represents the original digamma"
πολύτροπον is uncertain - much turned, much traveled, wily, complicated, shifty etc.
μάλα - strengthening adverb. Very, greatly, modifying πολλὰ. μάλα πολλὰ here is, I think, "very much", so "wandered very much".
2
πλάγχθη - πλάζω aorist passive with dropped augment. In passive, πλάζω is "wander, roam" while in the active voice it is "to turn away from"
πτολίεθρον - Epic for city
ἔπερσεν - πέρθω to sack/destroy. θ + σ = σ
3
ἴδεν - Epic aorist (without ε) of εἶδον, which is already an aorist. Highly irregular with other parts provided by different verbs (ὁράω and ὄψομαι)
νόον - attitude, way of thinking - Fritz
ἔγνω - 3rd person aorist of γιγνώσκω. Very irregular.
4
ὅ γʼ - the ὅ refers to the previous subject and it is often used with γε or δε in Homer as a strengthener.
πάθεν - missing augment
ὃν κατὰ θυμόν - I'm not sure what the ὃν is doing here. Look this up later.
5
ἀρνύμενος - ἄρνυμαι present participle. Gaining, struggling, trying to gain,
ἥν - possessive pronon = ἑήν. So ἥν τε ψυχὴν = his life/soul/spirit
ἑταίρων - of his companions
