What is the name of the fictional book that records Bilbo and Frodo’s stories in Tolkien’s legendarium?

The fictional book that records Bilbo and Frodo’s stories is The Red Book of Westmarch.

The Red Book of Westmarch is Tolkien’s imagined source for much of The Hobbit and The Lord of the Rings. Bilbo begins the original account, writing about his journey to Erebor and his discovery of the Ring. Frodo later expands the record with the history of the War of the Ring, and Samwise Gamgee contributes to its completion.

The title refers to the red leather-bound volume that Bilbo brings back to the Shire and to the Westmarch, a region of the Shire associated with its later preservation. Tolkien presents himself as an editor and translator of material derived from this fictional manuscript, adding a layer of historical realism to the narrative.

The Red Book is not the same as the Book of Mazarbul, which is a damaged Dwarven record found in Moria. Nor is it a title for The Silmarillion, whose imagined textual history is separate and much broader in scope.