Another cool building in Hong Kong.
Warning: Spoilers ahead.
The beginning of the show centers around Martha Jones’ life and the problems that she faces because it’s her brother’s 21st birthday party, and her divorced parents are squabbling again.
The Doctor checks himself into a hospital in London, right before the whole hospital is sent off to the moon for some strange reason. Martha Jones examines him and notices his twin heartbeats just before they are sent off to the moon.
This happens because the Judoons, police for hire, are looking for a plasmavore. The Judoons do not have any jurisdiction on Earth, so they moved the hospital where they knew the plasmavore was hiding to the Moon. The plasmavore is also an internal shapeshifter, meaning that after it ingests human blood, it can mimic human internal organs and hide among the humans. The Doctor meets Martha Jones, who is an intern and who helps him out. She tags along and provides interesting insights to the situation.
Since he is a Time Lord, he is in trouble because they will disintegrate him if they find him. So he kisses Martha and forces an exchange of bodily fluids, making the Judoons use a higher scanning frequency. Thus, they find the plasmavore, right after she emptied the Doctor of all of his blood. However, since the plasmavore thought that he was human, she now has Time Lord blood in her, and will register unhuman. Right before being disintegrated, the plasmavore connects her doomsday device, which will kill everybody on the Moon and on the light side of Earth.
Martha Jones reanimates the Doctor. Either that or he was just in suspended animation. The Doctor has just enough strength to deactivate the device. The Judoons put the hospital back on Earth and she agrees to go with him on a trip.