You may also enjoy "Master of the Five Magics" by Lyndon Hardy.Fantasy written by a physical scientist -- the universe envisaged has five different types of magic spanning many of the types you specify. Some of them are like slightly different forms of science we know (e.g. they have Alchemy which is like alchemy but works and sort of like chemistry, they have thaumatergy which is sort of like physics) and they have others that involve supernatural powers but are still bound by laws and principles.It's not great writing but it is the best attempt I know to create a set of laws for magic that have rationale and consistency.There's (trying to avoid spoilers) a sixth magic that isn't any of yours but is pretty much what you'd come up with once you'd enumerated yours. There's a sequel "Secret of the sixth magic" that goes into more detail. I think there's a third in the trilogy but I never read it.