'\'Warning: Wikipedia contains spoilers.''
The book is divided in three main parts (originally published in magazine form as three consecutive stories), on Earth, on an alien world (in a different universe with different physical laws), and on the Moon. The main plot line is a conspiracy by the aliens to alter physical laws in our universe, with the final aim of turning our Sun into a supernova, and collecting the resulting energy for their use (the reader only knows about this plot roughly at two-thirds of the book). Humans initially fall for the trap, but in the end the protagonist will understand the danger and will find a solution that will harm no one and greatly benefit humanity.
The most notable part is the alien world exploration. Asimov rarely describes aliens, preferring tales of humans and robots, but this time he goes into considerable detail. His aliens have three sexes with fixed roles for each sex. They are quite immaterial and can compenetrate each other, mainly for sex. They feed off sunlight and are discovering artificial light just now. A group of three forms a triade that, after producing three children, will fuse into a "hard" being, which would be the adult, more intelligent form.
Their universe is different because strong nuclear force is much higher. Therefore, their stars are much smaller (a star like ours would explode immediately), and they try to exploit this difference with our universe in the manner outlined above. The solution offered by Asimov is to find yet another universe, not inhabited, where physical laws are different in the opposite direction, and use that as a balance.