In this post you'll be able to see clearly the steps of Ulysses' journey and how long he spent in every spot of the Aegean Sea. 

Bear in mind that it tells of events that supposedly occurred in the Mycenaean period (XVII century BC - XII century BC) while Homer is said to have written them down in the Archaic period, around the 8th century BC. 

For this reason, it is impossible to find the dates on which each of the events narrated took place. However, we can know how much time Ulysses spent in the different stages of his journey because of the numerous time references he makes when telling his story. Moreover, this platform doesn't allow us to write numbers with less than four digits. Therefore, in this timeline the dates are arranged in this way, being the year 1001, the year in which the Trojan War begins, as it is the beginning of Ulysses' journey, even though it isn't even set in the right millenium