Arthur C. Clarke's Mysterious World

This episode introduces the themes that are explored in the remainder of the series. Clarke expounds on his categorisation of mysteries, self-consciously aping the famous 'close encounters' categorisation used by some ufologists:

1. Mysteries of the First Kind – phenomena which were mysterious to our ancestors but are now well understood. Clarke illustrates this category by observing the Solar eclipse of 16 February 1980 from Hyderabad, India, highlighting that eclipses are still treated with reverence and suspicion in some cultures.
2. Mysteries of the Second Kind – phenomena which are as yet unexplained, but where we have several clues that hint at an answer. Clarke looks at ball lightning (including one sighting by Roger Jennison in the cabin of an aircraft), the Loch Ness Monster, Remy Van Lierde's encounter with a gigantic snake, a sighting of a sea serpent off the coast of England, the stone spheres of Costa Rica, the Baghdad Battery, the vitrified forts of Scotland, Stonehenge, and the Cerne Abbas Giant. The ruined ancient palace of Sigiriya in Sri Lanka, which Clarke mentions at the beginning of the episode, could also be included in this category.
3. Mysteries of the Third Kind – phenomena for which we have no rational explanation. Clarke mentions psychic phenomena as something that would be included in this category, and the extremely strange phenomena of raining animals and seeds and nuts "raining" from the sky might also be included.

This show is concerned with technology from history that was either ahead of its time and subsequently forgotten, or artefacts which are mysteries in themselves. This includes the Baghdad Battery, where German scientist Arne Eggebrecht is shown electroplating a small silver statue with a gold cyanide solution and a replica of the battery using grape juice. There are also segments on the Antikythera Mechanism (including an interview with Derek J. de Solla Price), the Stone Balls of Costa Rica and the so-called 'Skull of Doom' which dominates the opening credits of the series. Also included are the vitrified stone forts of Scotland including Tap o' Noth near Aberdeen.

This episode is divided equally between considering evidence for the Bigfoot and Yeti. Interviewees for the segment on the Yeti include Don Whillans, Lord Hunt and Eric Shipton. Lengthy consideration is given to the Patterson–Gimlin film, and interviewees include Grover Krantz – who demonstrates several casts of alleged Bigfoot tracks that he feels bolsters his belief that the creature represents a relative of Gigantopithecus.

Including Mokele-mbembe, giant anaconda, Ameranthropoides loysi as well as sightings and excavations of animals such as the moa and the woolly mammoth.