This book is one of the very best Sci-Fi books I've ever read. It ranks with Orson Scott Card's Enders Series, CW and CSL. Perhaps in many ways it's better than Card's books.
Clark's imagination takes us from the dawn of our Galaxy to its twilight and imagines possible futures beyond. It reads like a prophesy of new heavens and a new earth. Indeed Clarke writes from his home in Sri Lanka in his preface notes that there is a 'prophesy' on the very last page of the book, the truth of which no one living will ever know.
The story is set billions of years in the future. I thought that Clarke did an admirable job creating technologies needed for his novel's future not in existence today and artfully skirting the details of what and how they work so that the story was not interrupted. Some futuristic novels are made just silly by the author's attempt at too much detail about time travel and the like. Some things that support life in The City could not be known by the characters- a fact entirely consonant with the story.
Somewhat predictable for Clarke are predictions about the future disappearance of all cults and religions. He usues the word 'myth' as something untrue, a lie. Yet science comes not to be the sum and meaning of existence. There arises a person who is Unique and who questions things. Now this was what for me made the book great. Clarke doesn't fall to pat answers about the absolute supremacy of science but has us consider what it is to be human by contrasting life in the last two cities left on planet Earth. With the actuality of eternal life, free from all ills and cares and worries for the comforts of life, free from the will to adventure and exploration, emotion and passion, would Man be human? What should a new heaven and a new earth be like? Perhaps the beginning will be the meeting of the two cities, two very different ways of life, integrating the best of each into both.
Perhaps it's all myth.