This poem is one of the poems in this publication that is said to be derived from traditions in Gondor, but a part of Shire-lore written down in the Fourth Age. The story features a mortal woman invited to join the elves and sail to "Elvenhome" An earlier version of this poem was published in 1934 and was called Firiel.
This story features a person who travels out to sea and is gone over a year in a mysterious land, which changes them as a person. It could be associated with the type of despair and darkness that is felt by people who have taken to the "wandering-madness" (p.258) which is a perspective of the Hobbits, making them "queer and uncommunicable" (p.258). This poem is a a revised and expanded version of Looney, which was published in the Oxford Magazine in 1934.
The poem "Cat" was intended as being a poem in the marginalia in the Red Book, a piece written by Sam Gamgee as a touched-up version of an older piece of "comic bestiary lore of which Hobbits appear to have been fond" (The Adventures of Tom Bombadil, p. 232). It is a fairly short poem so I have quoted it below in it's entirety instead of writing a summary of it which would be only one sentence short.
Fastitocalon is based on an earlier poem. This version is a reduced text, something that would suit hobbits as part of old bestiaries, framed as an adaption of possibly more learned elvish lore. Tolkien was inspired by a fragment of Anglo-Saxon bestiary.
The poem Oliphaunt is in the Lord of the Rings story recited by Sam Gamgee in The Two Towers (Book IV, Chapter 3), the volume where it was first published. Sam Gamgee explains "That's a rhyme we have in the Shire [...] we have our tales too, and news out of the South, you know." This bestiary poem is related to an earlier one imagined by Tolkien called Iumbo.
This poem depicts nightmarish creatures called Mewlips and the depressing route one takes to their dwelling and what happens when you reach it. There exsists a precursor to The Mewlips, it is called Knocking at the Door: Lines Induced by Sensations When Waiting for an Answer at the Door of an Exalted Academic Person. Tolkien published that one under a pseudonym in Oxford Magazine (1937).
This short poem is described as having been written into the marigins of the Red Book. It is supposed to depict a hobbit's idea of what an elf-maiden is. A precursor of the poem, called The Princess Ni, was published in the collection Leeds University Verse 1914-24.