Scott Jenkins, University of Kansas, in Philosophy Compass.
"Friedrich Nietzsche’s theory of eternal recurrence is an essential part of his mature philosophy, butthe theory’s metaphysical commitments and practical implications are both obscure. In this essay I consider only the metaphysical elements of the theory, with the aim of determining whether it is possible that we live our lives infinitely many times, as the theory maintains. I argue that the possibility of eternal recurrence turns on issues in personal identity and the metaphysics of time. As I proceed, I also consider the relation between Nietzsche’s theory of eternal recurrence and theories of recurrence found in the work of Heraclitus, the Pythagoreans, and the Stoics."
See Nietzsche, Beyond Good and Evil, in Great Books of the Western World (second edition, 60 Vol., 1990) volume 43