Moving on to the Late Eocene period 36 million years ago and mammals have prospered and are now the largest creatures on land and sea. This is an era of animals like andrewsarchus, the biggest mammal carnivore ever to walk on land, and the brontotheres, small-brained herbivores. It is in the sea, however, that the most monstrous mammals of all can be found. We follow the fate of a female basilosaurus, a huge serpent-like early whale, but nothing like the gentle filter feeding whales of the 21st century. Four times the length of the great white shark, with jaws to match, she is every inch a killer.

25 million years ago the biggest land mammals of all time, the indricotheres, stalked the Earth. Up to seven metres tall and weighing 15 tonnes, adults were too big to be eaten by any predator of the time. Only in the first few years of its life was indricotheres vulnerable. The programme follows the fate of a calf from his traumatic birth to see whether it can survive droughts, killer hogs and hyaenodon - a predator the size of a rhino with jaws that could crush a rock.

Moving on to Ethiopia 3.2 million years ago, we witness the beginnings of mankind via a group of australopithecus - a type of ape which, like us, walks upright on two legs. But unlike us, these early members of the human family weren't predators, they were prey. Things get worse for the group as they are hunted by a sabre-tooth cat called dinofelis and fall victim to other dangers such as malaria, rival australopithecus and a rampaging 14-tonne deinotherium.

Back one million years ago, South America was a continent of exotic oversized creatures found nowhere else on Earth - huge terror birds, giant ground sloths and spiky-tailed relatives of the armadillo as big as cars. The deadliest animal of them all was smilodon, the largest of the sabre-tooth cats, with canines like carving knives. The programme follows the fortunes of an individual male, Half Tooth. Ousted from his clan by a pair of rival males, his life suddenly becomes a struggle to survive in this alien world.

Travelling forward in time to 30,000 years ago, it's the middle of an ice age. The landscape is dominated by mighty mammoths, living side-by-side with woolly rhinos, giant deer and two separate species of human. The programme follows the fate of a herd of mammoths in their annual struggle against the harsh ice-age conditions. Every summer they spend on the grassy plains of what will one day become the bottom of the North Sea, but every winter they are forced to head for the less exposed valleys further south. It is a journey fraught with danger: mammoths can get trapped in frozen bogs, and the herd must run the gauntlet of hunters like cave lions and the deadly Neanderthals.

This is the story of a book that could have changed the history of the World. To the untrained eye, it is nothing more than a small and unassuming Byzantine prayer book. For faintly visible beneath the prayers on its pages are other, unique, writings - words that have been lost for nearly two thousand years. The text is the only record of work by one of the world's greatest minds - the ancient Greek, Archimedes - a mathematical genius centuries ahead of his time. Hidden for a millennium in a middle eastern library, it has been written over, broken up, painted on, cut up and re-glued. But in the nick of time scientists have saved the precious, fragile document, and for the first time it is revealing just how revolutionary Archimedes' ideas were. If it had been available to scholars during the Renaissance, we might have reached the Moon over a hundred years ago.