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he nearly filled it's pages with his account of the war. But annexed it and preserved with it, probably in a single red case, were the three large volumes, bound in red leather, that bilbo gave him as a parting gift."
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I think what it's saying it is Bilbo's three volumes, and what Frodo wrote down in the book is what makes up the Red Book. Frodo left Bilbo's stories alone, added in his own stories, creating the "Red Book of Westmarch," the most important source for the history of the war of the ring.