In the books 5 to 12 Odysseus’ character does not really undergo any transitions from one facet to another. Odysseus still carries the same attributes and traits right through to the end of the story. It is, however, evident in book 22, when Odysseus takes his revenge upon the suitors, that we see a totally different side to Odysseus’ character. Both these two points will be addressed in this answer.
At the beginning of the Epic, Odysseus is presented as a very brave and heroic man who often thinks about his home, wife and son. He is a character that loves story telling, which also includes lying with the greatest of ease. Odysseus “the man of many resources” never changes in his ways throughout the rest of the Epic, as he remains constant to all his former attributes. In this way it is obvious that Odysseus is a very stable hero who acts and thinks in the same manner always, much like any human.
However, there is a twist to this debate, as in Book 22 when he fights the suitors and prevails we do see a very different side to the character of Odysseus. In this book, Homer presents Odysseus to us as a very ruthless and un-forgiving character one who has everything set on destroying all he can. Odysseus could basically be described as heartless. We see this in particular when Odysseus “stuck Leodes full in the neck.” Leodes had submitted to Odysseus yet he was blessed with no hope of recognition as Odysseus had already decided upon the suitor’s fate. This is quite a change in the way that Odysseus is portrayed in all the other episodes of The Odyssey.
From this it is clear that the answer to this question is very double sided. As Odysseus does not particularly change, however in a sense he does. It is quite clear that the answer could be either way. I believe, however, that as Odysseus does not change for the majority of the Epic, he is therefore a character that does not seem different as the books progresses.