An experiment is conducted on an artificial mini-world in space to find out if an Artificial Intelligence delegated with running humanity's affairs could take over.

Longer synposis from the back of the first paperback edition:

Civilization had grown so complex that only a world-wide computer network could control everything. But the computer was only logical--it lacked common sense. Ad its all-to-logical decisions were beginning to cause too many near-fatal accidents.

The solution was on the drawing-boards—a universal, self-aware and self-programming computer, equipped with judgment. But… Could it be controlled? Or would it attempt to take over, disregarding its creators? If so, could it be turned off?

Raymond Dyer and his team of computer specialists knew they had to find answers to these questions, but eh project was too dangerous to test on Earth. So they installed the super computer on an orbiting satellite and programmed it to survive at all cost. Then they sent a group of men to attack the computer… to goad it into trying to kill them. Them they would turn it off.

Obviously if things went wrong, they might lose a few men,--but the satellite and the computer could always be destroyed.

Obviously…

But the computer didn’t quite see it that way!