The Legion of Time
by Jack Williamson
Sphere, London, 1977

First published as a magazine serial in 1938, this is a competent action adventure story
in the SF tradition of its day, remarkable for only one thing. This apparently was the first time, in fact or fiction, that the concept of parallel worlds, later to become the many-worlds interpretation of quantum mechanics, appeared in print. Of course, there are older "what if" stories set in alternative realities, but Williamson used respectable scientific language to set his scene, only a decade after the foundations of quantum mechanics had been laid.

"Geodesics have an infinite proliferation of possible branches, at the whim of subatomic
indeterminism." Hugh Everett, in his doctoral thesis nineteen years later, couldn't put it any more succinctly, although he did put it on a secure mathematical footing. It's seldom that SF really does anticipate the advance of theoretical science, and well worth noting when it does happen.

Article about Geodesic Domes and Charts of the Heavens

The Man in the High Castle
by Philip Dick
Gregg Press, Boston, 1979

A parallel-reality story set in a world where the United States lost World War Two. Nicely written with minimal science but a slight twist that takes it out of the ordinary.

The Man Who Folded Himself
by David Gerrold
Amereon, Ltd., Mattituch, New York, 1973

A funny and entertaining portrayal of the confusing effects of travel forward and backward in time among the many worlds of perpendicular reality. It's easy to dismiss the "science" in this as hocus-pocus, but the implications are very close to some of the ideas presented in John Gribbin's book about quantum physics, In Search of Schrodinger's Cat, (Bantum Books, New York, 1988)

Pavane
by Keith Roberts
Hart-Davies, London, 1968 (paperback Panther)

Perhaps this story is set in a parallel universe, perhaps not. Either way is makes good reading.

The Schrodinger's Cat Trilogy:

The Universe Next Door
The Trick Top Hat
The Homing Pigeons
by Robert Anton Wilson

Pocket Books, New York, 1982

It is almost impossible to describe this funny, irreverent, and brilliant trilogy in which three different variations on the quantum theme (one to each volume) are applied with scrupulous care to provide the framework for more or less the same set of actions involving more or less the same set of characters. In a way, the trilogy does for quantum throry what Lawrence Darrell's Alexandria Quartet did for relativity theory.....but Wilson is funnier. An acquired taste, but if you can acquire it you will have the true flavor of the quantum world on your tongue.

Timescape
by Gregory Benford
Pocket Books, New York, 1981

The best portrayal in science fiction of what it is like to be a research physicist, combined with a superb fictional portrayal of the kind of time travel that may be possible in a many-worlds reality.

Too Many Magicians
by Randall Garrett
Ace Books, New York, 1981

"What if" stories set in a parallel reality where Richard Lionheart survived for long enough to ensure that the succession to the English throne did not pass through his brother John. Scientifically slight, but good-detective stories, and fun.