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Rough sketch of Quickstart guides:
Crash course for new viewers who just want to start with the 60th
Doctor Who is a British Sci-Fi show spanning 60 years focusing on an alien, The Doctor, who travels through space and time in a time machine that takes the form of a police box that's bigger on the inside than the outside, often accompanied by humans in their adventures. When The Doctor is about to die, they can avert death by changing their face and slightly alter their personality, allowing the show to continue onwards as actors and writers change.
Going into the 60th anniversary The Doctor has reverted to one of their past faces for the first time ever, one of the most prominent actors in the role, David Tennant, returning for a trio of specials.
Also returning are the well-loved Catherine Tate as Donna Noble, a previous traveling companion of Tennant's Doctor who has had her memory erased in order to save her life and Bernard Cribbins, who passed away in 2022, in a posthumous appearance as Wilfred Mott, her grandfather.
Section for getting up to speed for those who left after Tennant (just plot - change name)
If you're coming back to the show for the first time since David Tennant left, let's real quickly go over the basic outline of the plot points you've missed during this time.
After regenerating into The Eleventh Doctor, played by Matt Smith, our Time Lord protagonist meets his newest companion, Amy Pond, during her childhood and helps her solve a problem, a crack in her house, a tear in time and space. He tries a short hop into the future - but finds himself flung years further than he thought, and reunites with Amy, played by Karen Gillan. The two travel on a few minor adventures, encountering River Song yet again, as more of these cracks in the universe menace them - even erasing a horde of Weeping Angels from ever existing. Amy's fiancé Rory Williams, played by Arthur Darvill, joins the group, before eventually becoming erased by a crack - Amy forgetting all about him. As The Doctor attempts to prevent the opening of a prison spoken in legend, the Pandorica, it becomes clear that the setup is a trap, the opening was timed to lure The Doctor so that he could be imprisoned. While he's in the Pandorica, his TARDIS explodes, creating the cracks in time, wiping out most of the universe. The Doctor escapes from the Pandorica, and uses the fragments of information stored within it to reboot the entire universe, using his exploding TARDIS as a power source, before showing up in this newly rebooted universe on Amy and Rory's wedding day.