Which nonsense poem by Lewis Carroll appears in 'Through the Looking-Glass'?

The Lewis Carroll nonsense poem in 'Through the Looking-Glass' is 'Jabberwocky'.

Alice encounters the poem early in the 1871 book, discovering it in a volume written in mirror writing. When she holds the pages to a mirror, the apparently unreadable text becomes legible. The poem describes a hero's encounter with the fearsome Jabberwock and is presented as part of the strange, inverted world Alice has entered.

Carroll had written an early version of the opening stanza years before the book appeared. It was printed in 1855 in 'Mischmasch', a family magazine Carroll produced, under the title 'Stanza of Anglo-Saxon Poetry'. He later expanded it into the poem known to readers today.

'Jabberwocky' is famous for its playful invented vocabulary, including words such as 'chortle' and 'galumph'. Humpty Dumpty later offers Alice explanations for several of the poem's nonsense terms, although Carroll's own notes do not always match those explanations. 'The Hunting of the Snark' is another Carroll poem, but it was published separately in 1876.