Story 1 - An Unearthly Child

In which Coal Hill schoolteachers Ian Chesterton and Barbara Wright are intrigued by pupil Susan Foreman. She is brilliant in some subjects yet makes elementary mistakes about other things. Following her home one evening, to speak to her grandfather, who is supposed to be a doctor, they find that "home" appears to be a junkyard, at 76 Totter's Lane - a junkyard with a battered blue Police Public Call Box in it.
Susan is nowhere to be seen, but the Doctor turns up. An old man with long white hair, dressed in old-fashioned Edwardian style garb, he is evasive and dismissive of their concerns. Susan is in the Police Box, and the teachers push their way in - finding themselves in a brightly lit futuristic control room. The Doctor is furious and fears they will expose his secret, and so he dematerialises the ship (which Susan has called the TARDIS).
In a prehistoric landscape, they are captured by a palaeolithic tribe which has recently lost the secret of fire-making. The leader, Za, is also in the midst of a power struggle with a newcomer name Kal. An old woman who fears the return of fire helps the time-travellers escape. Za and his bride-to-be, Hur, give chase. Za is injured in an animal attack and the travellers stop to help him - leading to their recapture.
Kal has killed the old woman, and is forced out of the camp. He returns and is killed by Za.
Ian makes fire for Za, hoping he will release them. When it appears that he won't, they frighten the superstitious tribes-folk with 4 skulls planted on flaming sticks. The diversion allows the travellers to escape back to the TARDIS.

This 4 part story, broadcast between 23rd November and 14th December 1963, was written by Anthony Coburn. The production team had serious reservations about using it to launch the series - fearing the viewers might not engage with a bunch of grunting cavemen.
Its biggest strength is the opening episode, which in only 23 minutes or so introduces the principal characters, the attributes of the TARDIS, and sets up the premise for the rest of the series. A couple of ordinary people, thrown unwillingly together with a strange old man and his grand-daughter, into a series of adventures in Time and Space.
Susan is the identification figure for the younger viewers, even though she is no ordinary schoolgirl. The enigma of her character is set up through an after school chat between Ian and Barbara, and through the use of flashback scenes. She knows a lot about chemistry, but not about something as humdrum as the British currency.
Sydney Newman had originally wanted her to be an Earth girl, but Coburn and script editor David Whitaker developed her as being an alien like the Doctor. Making her his grand-daughter was added to get round why a young girl would be travelling around with an old man.
Ian and Barbara are also audience identification figures - this time for the adult viewers. Ian, a science master, is a natural born cynic - refusing to believe the Doctor and Susan until he steps out onto the stone age world.
Barbara, who teaches History, is far more ready to accept what is going on. The choice of their academic subjects was an important one - Ian would be able to comment on science matters in the futuristic stories, and Barbara in those stories set in Earth's past.
The Doctor is abrasive, rude, and threatening initially - though less so than in the aborted "pilot" version. He resents the presence of the teachers in his "home" and in his life. Later in the adventure he appears to be jealous of Ian's leadership qualities - and Susan's admiration for him. (An original idea had been for Susan to have had a crush on him).
Alarmingly, at one point the Doctor appears capable of murder. When Za has been injured by the animal in the forest, the Doctor wants to leave him to his fate - concerned only for is own safety. When the others refuse to leave the wounded man, he picks up a sharp stone. We - and Ian - are left with the impression that he intends to finish Za off.

The Doctor is seen to be a pipe-smoker in this story - never revisited - and this is probably just there to get the principals involved in the fire-making plot. Kal - Doctor Who's first villain - sees him using matches and so abducts him, and the others follow. The tribal politics are interesting, though it is fortunate that they only take up 3 episodes. Concerns that the characters would be grunting cavemen are unfounded. Some of the language is quite poetic.
There are captures, escapes, chases and fights - all to become staple elements of the programme and the sort of adventure necessary to capture a family audience's attention.
Unlike other genre shows, the solution to the time-travellers' predicament is achieved through brains rather than brawn. They don't beat up the tribes-people and run off. Susan gives Ian the idea for the 4 flaming skulls. The Doctor is not yet the hero in his own programme - this role is very much Ian's for now.

Cliffhanger episode endings would become an important element of the programme.  This story has the following:

1. An Unearthly Child - the arrival of the TARDIS in a bleak landscape, with the ominous shadow of a watching figure.
2. The Cave of Skulls - the travellers trapped in the titular cave, the skulls showing evidence of great violence.
3. The Forest of Fear - cut off from the TARDIS by a group of armed tribesmen.
4. The Firemaker - the ship's radiation meter rises to the danger level, unnoticed by the travellers.

Having a cliffhanger leading into the next story was established here and would be the norm for much of the first couple of years of the programme. 

Barry Newbery designed the story (following Peter Brachacki's designs for the opening episode) and he does a sterling job in the cramped Studio D, Lime Grove - creating an impressive forest set along with the cave areas and the TARDIS landing site.

Things you might not have known:

• The TARDIS prop is smaller than real Police Boxes due to it having to fit into the studio lift.
• The male tribe actors were asked to show their chests and legs at audition. Hairy got you the job.
• One cave woman extra quit rather than wear the costume and make-up.
• The TARDIS gets stuck as a Police Box for the first time in this story - as we see from the Doctor and Susan's reactions.
• It is only ever assumed that this is prehistoric Earth - it is never stated, and so could be a primitive tribe on an alien world.