The Dancers at the End of Time

First American publication of the trilogy, since expanded:
AN ALIEN HEAT:
From a region believed to have been a province of legendary New York City, a magnificent reproduction of the Great Fire of Africa draws Jherek Carnelian into a very different kind of inferno, plunging him back through the aeons to the heart of Victorian England.
THE HOLLOW LANDS:
Far beneath an ancient Earth is a youthful paradise stuck in Time, ruled by a robot of ageless wisdom, invaded by brigands fearsome & foul. They pursue the lovesick Jherek Carnelian to the fin-de-siecle London of yesterday & thence to lurid Paleozoic seas. Then ahead to the final days of the Universe in a mighty drama of hallucinatory magnificence where immortality is assured, science is sexual & sex is megamorphous.
THE END OF ALL SONGS
Dying cities flare and sputter in Earth's last days, as alien beings invade with demented plans for salvation. Delirious gods celebrate fantastically, and Jherek Carnelian searches the vast seas of time for sanity, peace & love, tho madness rules a senile universe.