Poem

A poem was a form of literature written by poets.

There were numerous styles of poems, including ballads and sonnets. The Ballad of Flannan Isle was mentioned and quoted by the Fourth Doctor while leaving Fang Rock. (TV: Horror of Fang Rock) He later claimed to have helped William Shakespeare transcribe Hamlet after the playwright had sprained his wrist writing sonnets. (TV: City of Death)

"The Lament of the Non-Operational" was a Dalek poem of one hundred and twenty-eight stanzas. (PROSE: The Also People)

Suzie Costello used Emily Dickinson's poem "The Chariot" as a lockdown code for the Torchwood Hub. (TV: They Keep Killing Suzie)

Silurian poetry consisted of optical illusions and mathematics. (PROSE: The Insidious Ideas of the Danger Thinkers)

The Twelfth Doctor once gave a lecture about poetry when he was supposed to talk about quantum physics. He later told Bill Potts that they were the same thing, "because of the rhymes". (TV: The Pilot)

The Judoon had nothing to compare to poetry. (AUDIO: Judoon in Chains)

Alternate timelines
An ode was another type of poem. "An Ode to Sarah Jane Smith" was written by Carla Morgan in an alternate version of Earth where Sarah Jane Smith died in 1964, at age thirteen. (TV: Whatever Happened to Sarah Jane?)