"Ulysses" is a dramatic monologue written in blank verse but it can best be divided into three sections. In lines 1-33, Ulysses (Odysseus) is thinking, thus an interior monologue, about his adventures and dreading a life of relative idleness. He does not find much meaning in his new life as a king, pronouncing rewards and punishments to his citizens who do not even know him or his truly adventurous spirit:
Matched with an aged wife, I mete and dole
Unequal laws unto a savage race,
That hoard, and sleep, and feed, and know not me. (3-5)
In the subsequent lines, Ulysses recalls his adventures, all the people and places he's seen, and he notes that these adventures and interactions have defined him. "I am a part of all that I have met." However, he notes that as his being has been defined by those adventures, now that they have ceased, his and others' conception of himself as that adventurer also fades. For Ulysses, he is what he does. Therefore, to be an adventurer, he must continue to venture. To cease is to become "dull" and to "rust unburnished, not to shine in use!" (23).
In the second section, lines 33-43, Ulysses continues the monologue by introducing his son, Telemachus, whom he says will eventually succeed him as king and be successful in that occupation. In fact, Ulysses believes that Telemachus' natural disposition is more suitable to being king whereas Ulysses is more naturally suited to be a warrior and a traveler. Thus, he concludes, "He works his work, I mine." (43).
In the third section, Ulysses turns his attentions from his lamentable present to the possibilities of adventure in the future. He addresses his traveling companions ("mariners") and implores them that their courageous days might not yet be over. "Some work of noble note, may yet be done, / Not unbecoming men that strove with Gods." (53-54). Ulysses acknowledges the passage of time and in spite of that, he urges his companions (and himself) to press on. He is willing to take the risk of adventure even if it kills him. Ulysses acknowledges that he and his men are older and weaker, so he's counting on their will power to embolden them enough to embark on an adventure again.
Ulysses is not just frustrated with his old age and his less than exciting retirement. He is genuinely anxious that he is losing a sense of himself and his zest for life by accepting this new idle life. In the end, he is determined to brave the struggle of adventure again. Ulysses believes that to do otherwise is to deny himself and to not fully embrace life. So, he determines to continue "To strive, to seek, to find, and not to yield." (70).