Forest of The Dead

The Doctor, Strackman Lux, Prof. River Song and the rest of her group successfully flee from the Vashta Nerada that were pursuing them at the end of "Silence in the Library". As the group light up the room to dispel the shadows the Vashta Nerada may hide in, the Doctor finds that the Library's moon is sending out electromagnetic signals that interfere with his sonic screwdriver. Lux explains that the moon acts as a virus checker on the Library's computer core, causing the Doctor to recognise that Donna and the other 4022 people who were "saved" according to the Library were actually stored in the data core. The group make for the access point to the computer core, still pursued by the spacesuits of Song's former team-mates possessed by the Vashta Nerada. The Doctor pauses a moment to try to reason with the Vashta Nerada, and learns that the books in the Library were made from the trees in which their species had laid its eggs. The Vashta Nerada awoke in the Library and now take it as their own forest to defend.
Meanwhile, Donna wakes up in the care of Dr. Moon inside the Earth-like computer simulation, though Dr. Moon as well as the little girl who watches Donna from her television attempt to prevent Donna from recognising it as such. Dr. Moon introduces Donna to a man called Lee, and the two become lovers, marry and have two children in a quick succession of vignettes. One day, Donna is met by Miss Evangelista, who explains that the Library had stored her persona when she was attacked by the Vashta Nerada, but due to corruption, her face has become severely deformed, although she has become more intelligent. She explains to Donna that she is no longer in the real world and proves it by pointing out that all the children around them including Donna's are the same boy and girl duplicated many times. The little girl causes a distraction to prevent Donna from learning the full truth, but Donna's confidence is shaken, and when her children doubt their existence, they disappear. Donna desperately seeks out Lee. The little girl, fearing that the truth may be known, "deletes" her father and Dr. Moon, and descends into further despair.
To convince the Doctor that he will one day trust her absolutely, River Song murmurs in his ear something which shocks him. The Doctor and his group reach the core as Lux explains that "CAL", the name they have been seeing associated with the core, is the girl who is watching them through her television. She is really his aunt Charlotte Abigail Lux. As a child, she suffered from an incurable disease and Lux's grandfather paid for the construction of the Library, hooking Charlotte to its computer to allow her to spend eternity surrounded by humanity's literature. However, now that over four thousand other persons are in the core with her, even the "doctor" moon cannot help to keep the computer systems going. The Doctor plans to connect himself into the core to provide the stability to allow the rescued patrons to be reconstituted, and has Lux prepare for their arrival. When the Vashta Nerada threaten to attack them, the Doctor negotiates a deal—that once he frees the people from the core, he will have humanity leave the Library to them forever. The Vashta Nerada initially refuse, but when the Doctor tells them to look him up in the Library, they fearfully accept, giving him one day to clear the Library.
River Song recognises that the Doctor will die if he attempts to put himself in the data core, and knocks him out, taking his place instead. When he comes to, she has handcuffed him so he does not stop her, and she points out that if he dies before meeting her a paradox will be created. As Song connects herself to the system, Donna attempts to reach her husband Lee in the simulation before it whites out.
The Doctor's plan works as expected as all the stored humans, including Donna, are returned to corporeal form, and Lux begins to transport the humans off the planet. Donna attempts to find Lee but just misses him before he is transported away. The Doctor mournfully leaves Song's diary and sonic screwdriver to the Library, but suddenly questions why he would have given her the screwdriver in his future. He discovers that the screwdriver has a Data Ghost device in it, and races to the computer core to transfer its data into the computer. River Song awakens in the computer simulation, greeted by Charlotte, Dr. Moon, Evangelista and the rest of her team, and thanks the Doctor.