I first read this book in 1961 and it holds up well. It takes place some 3000 years in the future where people on an overpopulated Earth live in gigantic cities (hence the title). However, Spacers live on fifty underpopulated planets.
The Spacers have established an embassy on Earth on the outskirts of New York, called Spacetown. The book goes into great length contrasting the culture of the Spacers verses the Earthers, and this is necessary to understand the significance and possible motive of the murder of a Spacer in Spacetown.
Plain-clothes man Elijah Baley is assigned the case and in an unprecedented move is partnered with a Spacer robot, R. Daneel Olivaw.
The book succeeds as both a great work of Science Fiction speculation and as a fine mystery. Asimov does not cheat the reader, providing many clues to solve the perplexing murder.
This robot novel introduces the human looking robot R. Daneel Olivaw who would appear in many other robot novels as well as the continuing Foundation novels. This book is top notch.