Richard Haliwell's diary was the diary of Victorian Captain Richard Haliwell, detailing the British Imperial Spacefleet's trip to the Moon in 1878. Haliwell began writing in the diary to provide an insight into how astral travel affected the travellers who experienced such a journey, recording both the facts of their discoveries and his own thoughts on what they witnessed.
This diary was discovered in the time safe by the Fifth Doctor and Turlough, prompting the Doctor to conclude that he would acquire the diary in his future and leave it in the safe for his past self. Having read through the diary to learn more about the lunar park that the expedition discovered upon arriving at the Moon, the Doctor stopped reading when he discovered a paragraph where he and Turlough introduced themselves to the expedition, not wanting to learn any more about their future in case they were tempted to change it and thus invalidate the diary's warning; by stopping where he had done, he reasoned that they would be free to act as they wished after making the initial introductions. Turlough accepted this warning when he found a small piece of paper in the diary with the words "Believe me, you don't want to know!" written in his handwriting.
Despite the Doctor's warnings, after Haliwell and Emily Boyes-Dennison were captured by the mysterious Warden who controlled the park, Turlough took the future diary from the TARDIS with the goal of impressing the Doctor with his insight into their current adversaries and using the information within it to rescue Haliwell and Emily.
Haliwell continued to update his diary while he was in captivity to explore his insights into their captors, which included recording his own feelings for Emily.
Information recorded in the future diary allowed Turlough to find and rescue Haliwell and Emily before they were killed by a robotic hunter, although he was initially concerned that he wouldn't get there in time when he read about his future actions ahead of schedule. When the Doctor and Turlough were separated from the main group, Turlough stopped reading his version of the diary as he became concerned that he might read on and find that Haliwell never heard from him and the Doctor again, as that could 'prove' that they might not get back to Earth. He also worried that the disappearance of the note he had discovered from his future self meant that he may be entering a timeline where he would die.
After the expedition had returned to Earth, with Queen Victoria's announcement that astral travel would go no further, Haliwell entrusted the Doctor with the diary, wanting some record of their journey to remain and trusting the Doctor's discretion. Having put the diary he had just received from Halliwell in the time safe to tie up the last temporal loose end, the Doctor asked Turlough to leave the version they had originally acquired in the TARDIS library (also revealing that he had discovered the note Turlough had written to himself in the Draco when it fell out). (PROSE: Imperial Moon)