The Odyssey can be broken up into three distinct sets of categories. The second two are useful, but both are necessarily over-schematic, since Homer himself never had any book divisions or other specific breaks in his work. The Odyssey was only separated into books at a much later stage in Greek history, in Hellenistic times, that is to say over 500 years after Homer's death.
The first schema is one which Homer himself possibly intended during the composition. The work can very conveniently be broken down into six four-book sections, as follows:
V-VIII: Odysseus among the Phaeacians
IX-XII: The Great Wanderings
XIII-XVI: Odysseus arrives in Ithaca
XVII-XX: Odysseus in the palace
XXI-XXIV: Grand finale
The second, as used by Lattimore and others, focuses more on chronology than on the convenience of having similar sized sections of the poem (on which, see below on oral poetry).
V-VIII and XIII.1-187:The Homecoming of Odysseus
IX-XII: The Great Wanderings
XIII.187- end: Odysseus on Ithaca
The final set of divisions is that with which we are most familiar, and it is this that we employ in the book by book synopsis of the Odyssey that follows, although for ease of access the table of contents divides them as in the first schema.