Countless different spoken, written, and gestural languages were used by different cultures throughout time and space. According to the Thirteenth Doctor, a minimum of 90,000,000,000 languages were spoken within the known universe of N-Space. (TV: Spyfall)
The Doctor had great expertise in linguistics; the Ninth Doctor once claimed to be able to speak five billion languages. (TV: The Parting of the Ways) Later, the Fourteenth Doctor claimed to know 57,000,000,205 languages. (TV: Wild Blue Yonder) However, the Doctor still utilised the translation circuit of their TARDIS while travelling through space and time, though this was often more for the benefit of their companions, (TV: The End of the World, Cold War) and of the more than 57 billion languages, the Fourteenth Doctor was still not knowledgeable of the language spoken on one spaceship when he was out of the translation circuit's range. (TV: Wild Blue Yonder) Even while travelling on the fringes of the known universe, they kept the TARDIS systems open for new languages. (TV: Spyfall)
Language was constantly evolving. When Jo Grant invented the word "telempathy" to mean a sort of telepathic empathy, and asked the Third Doctor if this was a word, he responded that it was now. (AUDIO: The Tyrants of Logic)
Dalek propaganda claimed that a single Dalek was capable of speaking over 300 languages at a time when most humans could largely only speak Earth standard. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)