And there's a book on theories of magic! This one is much more recent, only three centuries or so, and it doesn't look as polished – more like someone's personal notes, bound for convenience and maybe shared with a few friends but not widely. The name matches Leareth's record-keeping name from the appropriate dates.
Vanyel and Leareth's world is known to have multiple planes, described as similar to parallel dimensions that have some permeability and interaction with each other. Mage-energy is a sort of universal fuel, able to affect the matter of any plane in a very large number of ways – and to build passages between them. Invisible to un-Gifted humans, it nonetheless behaves somewhat like water, gathering into river-like ley-lines and eventually into dense, turbulent 'nodes' of power. What makes a person Gifted is that they possess 'channels' in their mind, which can take in mage-energy and direct it to some useful purpose.
Different planes have widely varying levels of ambient mage-energy. Human mages and those of other intelligent races can, via using mage-energy form purely mental projections to other planes.
The plane where humans live is generally called the mundane or material world. The spirit world, also referred to as the Moonpaths and/or Ethereal Plane, is believed to be where dead spirits reside, although they're difficult both to find and to communicate with even for Gifted people capable of visiting. There are additionally four Elemental Planes (Earth, Air, Fire, Water), named by some long-dead mage for metaphorical resemblance and not because the comparable mundane substances originate there. All are much 'hotter' than the mundane world, in terms of their density of ambient mage-energy. Beings of varying levels of intelligence and power live there, able to dimly sense the mundane world, and mages can summon them by opening a passage that allowing said being to project a magically-constructed body.
The Abyssal Plane is host to 'demons' (an image of something with a random-seeming body plan consisting mostly of legs and eyes), which can also be summoned, although they're very stupid and the only reason to do so is if the mage wants something dead in a messy and disturbing fashion. The Empyreal Plane is believed to exist, and be the primary home of the gods (which are fully multiplanar beings, able to influence all of the other planes), but outside the reach of mages.
There's also the Void, which is a sort of sink – adjacent to all of the planes, it becomes the eventual resting place for all mage-energy, which is eventually returned via some sort of weather-like cycle that isn't fully understood even by Leareth. His top theory is that living things (in all planes), known to be generators of excess mage-energy, are actually pulling from the Void. Space is known to behave differently in the Void; Gates exploit this by routing through the Void to link two places that are distant in mundane-world space.
Leareth adds the novel hypothesis that the sentient races in the mundane world – those capable of Mind-Gifts – are also multiplanar beings, that a 'Mind plane' exists, separate from the spirit world, and that humans and other races have metaphysical appendages of some kind extending into it. He thinks that routing through this plane could explain why Mindspeech and similar Gifts are so widely found, and how a Thoughtsenser can read the thoughts of anyone, Gifted or not.
Leareth also theorizes that the Gift of Fetching, the part of it where objects can instantly be transported long distances, works by cutting through the Void in a similar way to Gates, though through a dedicated mind-channel that doesn't leak characteristic Void-energy in the same way.