This is a story of one man's attempt to survive in a post apocalyptic world.
Post apocalyptic stories seem to fall into one of two categories. Either humanity is humbled by some huge disaster that nature has thrown at us or else humanity is the victim of its own foolishness, a disaster of its own making. This story falls very much in the latter category.
The nature of the catastrophe is this: An accident whilst nuclear testing in space has somehow raised the radiation level on earth to the extent that it has either sterilized everyone or only allowed horrifically deformed monstrosities to be born which were at first eugenically eradicated and then later fought over as it became apparent that in them lay humanity's only hope for the future. Consequently, society has collapsed and the population is aging with the youngest people being at least 60.
It uses a somewhat tired premise in that humanity has attempted to wield a technology beyond our ability to safely control and which led to our own downfall. Although it is more than that; it is a lament against Aldiss' own age: "It was really the generation before hers that was more to blame, the people who were grown up when she was born, the millions who were adults during the 1960's and 70's. They had known all about war and destruction and nuclear power and radiation and death - it was all second nature to them. But they never renounced it."
The story's misanthropy goes deeper than that. Our society was so deeply flawed and corrupt that the disaster was almost a blessing, clearing the slate and allowing us to regain our humanity. As one character suggests: "Have you thought of the world we were born in, and what it would have grown into had not that unfortunate little radiation experiment run amok? Would it not have been a world too complex, too impersonal, for the likes of us to flourish in?" He adds: "Is not this rag-taggle present preferable to that other mechanized, organized, deodorized present that we might have found ourselves in, simply because in this present we can live on a human scale?"
All in all it is a kind of rambling tale with no conventional form of plot and conclusion to be reached at the end. This is more a mediation on the time and follows a brief transition of Greybeard as he follows his dream. Not much in the way of action but it certainly gives you plenty to think about.