In this essay I'd like to consider the implications of Odysseus' refusal to simply accept Calypso's offer of immortality and what it means to be individual. Moreover, I would like to compare this matter with the situation of Achilles in the Iliad. To start with it should be mentioned that both Odyssey and Iliad are immortal poems of excellent Old Greece poet Homer and in both these poems consider the life and exploits of great heroes like Odysseus and Achilles. It can be said that Odysseus in Greek mythology was the king of Ithaca and famous participant of the Trojan Conflict, the brilliant and resourceful orator. Also, Odysseus is one of the main element personas of the Iliad, the hero of the poem "The Odyssey" that tells of long years of wandering and comes back of Odysseus to his homeland.