While cleaning up the school library, Luso comes upon a strange book. Upon reading it, it is revealed to be a Grimoire which transports him to the world of Ivalice in Final Fantasy XII. Luso loses track of the Grimoire during the transition.
Luso soon finds he is in possession of another magic book: a journal that is recording his experiences, which he keeps on him at all times. Illua later recognizes it as the titular Grimoire of the Rift. As he completes story missions, the Grimoire fills itself out. It is temporarily lost when Illua's interference causes it to warp Clan Gully to Zellea, but Lezaford is able to return it to Luso. In the end, Luso is able to use its power to return home.
Illua also has her own Grimoire (though it is never properly explained, it may be the one that warped Luso to Ivalice), and seeks to use the Grimoire of the Rift to open the rift, which would release the entity Neukhia.
Interestingly, in the ending the Grimoire's place on the Library table has been taken by the journal Luso was assigned as homework.