Fletcher Pratt and L.Sprague deCamp were well-known authors of science fiction and fantasy in the Golden Age. Separately they both produced well-respected works for many years. But together they created something truly amazing: the world of the Mathematics of Magic, featuring Harold Shea and Reed Chalmers – two masters of mathematical logic who theorize that mathematics and logic and perception dominate reality, and thus if one can encode the logic of a particular world into one's calculations, one could in theory travel to the world so described.
Harold decides that theory is all well and good, but it means nothing if it's not tested. So he carefully follows the guidelines he and Reed have determined, and focuses on the postulates and mathematical guidelines…
… to find himself suddenly in the land of Norse mythology.
From that beginning, Fletcher Pratt and L. Sprague deCamp take Harold and, eventually, Reed, on a wild ride through the cosmos of fiction and myth that ranges from the coming of Ragnarok to Irish myth, Coleridge's Kubla Khan, Orlando Furioso, and beyond.
This story was one of the first truly multiversal stories I ever read, and I found endlessly fascinating because of two concepts that resonated very strongly with me: first, the existence of unlimited numbers of universes, some derived from (or perhaps inspiring!) our own fiction, and second, the existence of logical, rational, scientific rules that could, and indeed must, govern even apparently magical interactions.
The latter was and is very important to me. A common comment made to people who find some aspect of a fantasy hard to swallow is "It's magic, man. Stop thinking so hard," or something to that effect. But to me, if the world depicted is in any way like our own – and is apparently containing human beings who are like our own – magic that is in any way usable implies that there are, in fact, reliable and knowable rules in its operation. Violating that by simply waving hands and saying "it's magic!" is a cheap violation of the reader's trust; it means that you can pretty much do anything and there's no actual tension that the reader can rely on to drive the story's action.
Another aspect of the stories which was and is terribly important to me wasthe important reminder to both reader and characters to watch out for your unexamined assumptions about the world. This bites Harold Shea on his rear end more than once early on, when he forgets that the basic principle of operation was to transfer him to a world whose natural laws are not the same as his own; he therefore takes a stainless-steel blade and a handgun with him to the world of Norse myth, figuring they'll be surprised by such things. He then discovers that the blade rusts and the gun doesn't work, because the underlying rules and logic of that world don't encompass firearms or our world's steel alloys. It then takes him a bit to realize that, correspondingly, this means that he can actually do magic – real, functional magic – because that's the essence of the logic and world-transforms he's enacted.
Narratively, this is a very useful concept. You can show your hero as someone who thinks things out, plans carefully, and still screws up because he/she is immersed in various associations and beliefs that don't accord with the situation in which they finds themselves. This is part of the essence of Digital Knight (soon to be re-released as Paradigms Lost) – Jason Wood carefully figures out various explanations and approaches for various things, to discover that sometimes they don't work because his assumptions are wrong. He has to change his assumptions and approach because the world is not what he thought it was; as Big Trouble's Jack Burton would put it, "I'm a reasonable man, but I've just experienced some very unreasonable things."
Pratt and deCamp played with their concepts in numerous ways. Another striking one was recognizing effects, within that universe, of writing something that was heavily inspired by another source. In his second adventure, Harold Shea falls in love with and finally marries Belphebe (warrior maiden from The Faerie Queene by Spenser). When the group travels to the world of Orlando Furioso, Belphebe disappears, to be discovered again as "Belphegor", a very similar character but with no memory of Harold; as The Faerie Queene was inspired and informed heavily by Orlando Furioso, Belphebe had therefore been forced into a similar role in the world of Orlando, but without the backstory of having met Shea, who was of course an outside element. Shea's attempts to restore her memory are a central part of The Castle of Iron, the story taking place in the Orlando universe.
By modern standards there are shortcomings of the stories – Belphebe, though reasonably strong and capable in her own context, is nonetheless a secondary character in most of her scenes, for instance – but they were very well-written and engaging stories that captured my imagination strongly and helped solidify the multiple-world concept in my mind (along with The Chronicles of Amber and some other works, such as Robert Heinlein's interesting though flawed The Number of the Beast).
If multi-world adventures are your cup of tea, grab your adventuring gear and hop aboard the "Syllogismobile" with Harold Shea!