Doctor Who: The Newbies Guide
This is the seventh and final story in Season 18.
The Fourth Doctor dresses in a rather bohemian outfit, notable for its long scarf. He is somewhat alien, willing to play the fool, and almost never gets on with authority figures. In The Armageddon Factor, the Doctor fitted a Randomiser to the TARDIS in order to stop a cosmic entity called the Black Guardian from finding him.
Adric is from the planet Alzarius in E-Space. He is a mathematical genius from a race with a high metabolism (which means he heals fast). In Full Circle he stowed away on the TARDIS.
Nyssa of Traken is the daughter of Tremas of Traken. In The Keeper of Traken she helped the Doctor and Adric to defeat the Melkur, a living statue that threatened their planet. The Melkur was actually the Master's TARDIS, and at the end of that story the Master took over her father's body and disappeared. At the start of this story, nobody knows Tremas's fate.
Tegan Jovanka is a new character who is introduced in this story.
Recurring and Historical Characters
The Master is a Time Lord and an enemy and rival of the Doctor. In Terror of the Autons he arrived on Earth and allied with the Nestene Consciousness to attempt to conquer Earth. He was stopped by the Doctor and UNIT. He has since come into conflict with the Doctor on many occasions. In The Keeper of Traken he was reduced to a deathly husk, and then possessed the body of Tremas of Traken. At the start of this story nobody is aware of his new body.
It is worth watching The Keeper of Traken to get the backstory of Nyssa, Tremas, and the Master. Although the important details are summarised in the above write-ups for those characters.