My first introduction to magical transportation was Zelazny's "Amber" series. There are two poles to reality: Amber, which represents Order; and the Courts of Chaos, representing Chaos. Each of these poles is represented as a kingdom in its own right, with a source of Power available to those who can use it. Amber has her Pattern. Chaos has its Logrus.
Between these two poles of reality are Shadows, which you can consider as an infinite continuum of worlds, more orderly toward the Amber end, more chaotic toward the Chaos end, and encompassing all that exists--including our own Earth. Each Shadow is separate from its neighbors, with its inhabitants normally unaware of any other reality but their own.
To those with the ability to use (or be used by) those Powers are accorded the ability to move through and amongst those worlds at will in three different ways. One can begin in Amber and simply walk or ride a horse (for example), using their will to change aspects of the world around them until they've arrived at their destination. This takes the longest of the three, but might be the only way to get somewhere.
A much-more grueling version of Shadow-walking is the Hellride, where one's concentration must be complete. It gets you where you want to go more quickly than a Shadow-Walk.
The next way is by use of a Trump, something along the lines of a Tarot card. If you've been to a place or know a person well enough to draw them on a blank card, you can make a Trump for that place or person. Then you look at it, concentrate on it, exert your will to make it real, and if you've done it right you get a little window onto that place or person, and can step through (or bring the other person to you). In the first five Amber books, the Trumps are treated as something exclusive to the Royal Families of Amber and Chaos, but in the second set we find all sorts of people using them.
The third way is the hardest, and seems to be used more by those initiated into the Pattern. You must walk along the Pattern to reach its center (I'll discuss this in a later entry, but it's a horribly grueling contest of your Will against ever-increasing resistance); then you imagine where you want to be and command the Pattern to send you there.
The next series to come along was Robert Asprin's "Myth" books. Like Zelazny, Asprin's universe is a continuum of parallel worlds, but he calls them Dimensions. Just about any reality you can imagine is out there, somewhere--and all you need is a way of getting around.
If you can use magic and know your way around, you can cast a spell for shifting from your current Dimension to another one. You've got to know your target Dimension well enough, though, or you might end up somewhere else--and it might be a world where magic or Demons (Dimension travelers) aren't welcome.
The other method is mechanical--a pre-spelled ring, for example, or something called a D-Hopper, which I still think is pretty cool. It's a rod, maybe a foot long, and with several dials along its length. Set the dials for your destination, press the button, and *ZAM* you're there.
The most-recent series I've really gotten into is Mercedes Lackey's "Valdemar." Her approach to magic is by far the most complex of the three, but there's only one way of using magic to get around (not including the levitated barges some of her characters use, since the barges are still pulled by horses or mules). We only ever see the one world--no parallel realities to speak of, unlike the other two authors' works.
A Gate is a quick, but energy-expensive, portal between two places. To cast a Gate, the mage must know their destination well enough to form a mental image of the place, and only the highest class of mage can summon and use the Power needed to invoke the Gate's spell and hold the construct open long enough to use it.
One really neat aspect of Lackey's approach is that magic energy affects the world around it--for example, opening a Gate can trigger spectacular and violent thunderstorms.
11 hours ago