By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems. Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

In episode two, Professor Brian Cox is off to India, where he assesses arguably the first evidence of rational thought in literature, the poetry of the Vedic monks. They pondered mankind's origins, realising there must have been a day with no yesterday - a day of creation - prompting the age-old question of where did the universe come from? Brian marvels that the universe seems to follow a set of rules, the laws of physics, allowing space to be considered on the grandest scale, travelling to the most distant, farthest reaches of the cosmos just by using our minds. Brian also visits Japan, and offers viewers the idea that man lives in just one of an infinite number of universes that are being made all the time.

It's a mystery mankind has struggled to solve since the beginning of history - is space infinite or might there be great cosmic border where everything ends? Groundbreaking cosmology and state of the art space telescopes, now suggest the Universe has a finite size and a unique shape. If this is true, there must be an edge to the Universe, and beyond that edge, there could exist a world beyond our wildest dreams.

Beginning with the origins of the universe in the Big Bang, Sagan describes the formation of different types of galaxies and anomalies such as galactic collisions and quasars. The episodes moves further into ideas about the structure of the Universe, such as different dimensions (in the imaginary Flatland and four-dimensional hypercubes), an infinite vs. a finite universe, and the idea of an oscillating Universe (similar to that in Hindu cosmology). The search into other ideas such as dark matter and the multiverse is shown, using tools such as the Very Large Array in New Mexico. Cosmos Update shows new information about the odd, irregular surfaces of galaxies and the Milky Way perhaps being a barred spiral galaxy

On a trip to the fortified Moroccan village of Ait-Ben-Haddou in the Atlas Mountains, Professor Brian Cox reveals how by watching the stars' motion across the night sky, it is quite natural for man to think he is at the centre of everything. That view was held for many ages, but innate human curiosity has eventually led to an understanding of mankind's true place in space and time, and an appreciation that Earth is not a focal point but a mere particle of rock in a possibly infinite expanse of space, 13.8 billion years from the beginning of the universe.

When we look up into the sky it appears we live in a universe that is filled with light. But scientists are now certain there is far more matter in the dark portions of our universe that we can’t see or touch. There’s something hiding in the shadows. Cosmologists agree that 'dark matter' has helped shape our Universe, but now they need to figure out what dark matter is. What’s going on in this hidden world? Could it have formed its own dark stars, planets, and even life forms? Could this Shadow Universe threaten our world of light?