The Rose was a house used as a theatre in 16th century England. The Doctor's TARDIS materialised on stage during a performance of one of Christopher Marlowe's plays. The audience, most of whom were drunk, applauded Marlowe's brilliance before the Fourth Doctor dematerialised the TARDIS. (PROSE: All Done with Mirrors)
In 1592, the premiere night of the play Richard III was performed at The Rose theatre, with the Ninth Doctor taking over the title role from playwright-actor William Shakespeare when the Doctor and Rose Tyler tried to save him from the Shadeys. This performance was interrupted when Robert Greene chased Rose and Shakespeare into the theatre, and planned to use the Shadeys' powers to destroy it, but the Doctor and Rose instead convinced Greene to save the world and send the Shadeys back to their own dimension. (COMIC: A Groatsworth of Wit)