Esperanto was a language invented by Polish oculist (ophthalmologist) Zamenhof in 1887. He intended it to be the universal language of peace. It was the only language that could not be translated by the Doctor's TARDIS. (AUDIO: A Thousand Tiny Wings)
The Master once went under the alias "Estro", an Esperanto word for "Master". The Eighth Doctor reflected that it was typical of the Master to corrupt something intended for good. (PROSE: Legacy of the Daleks)
The idea of a universal language like Esperanto was not exclusive to Earth. The Fourth Doctor once called Trillic "a sort of cybernetic Esperanto". (COMIC: The Wreckers)
River Song suggested that the Eleven ought to have named himself more creatively, giving "Dek-Unu", the Esperanto word for "eleven", as an example. (AUDIO: The Sonomancer)
When the Fourth Doctor reassembled Sir Robot, he sometimes spoke in Esperanto. (PROSE: Doctor Who and the Krikkitmen)
Pyke-Xi Raul spoke Esperanto and tested if the Petaloudepta understood it. (PROSE: Wringing Off)