The book does tend to assume you come in already knowing what types of mana there are, but in the course of describing how pairs of mana types interact, it does tend to at least mention the existence of a whole lot of mana types!
There is not a neat taxonomy of basic magical types the way there is a taxonomy of 511 chemical elements; there are standardized kinds of magic that get used in common spells, but they are not ontologically exhaustive. It's like chemistry where you don't know about atoms, and instead you stare at a particular chemical that a sorcerer or another wizard or a magical artifact output, until you can make something the same flavor yourself. It's like kitchens; there are standard spices but they are not exhaustive of all possible spices.
Falash isn't mentioned in the book; it may possibly be a thing for when you want sorcerers charging your artifacts, and sorcerers are quite rare. There's discussion of a different kind of magical charging port that would take less complicated wizardry from people who can't just will magic into place; and then a simpler yet kind of battery that can be charged by complete yahoos throwing magic at it without knowing any wizardry at all. Not very efficiently, but sometimes you care less about "efficient" and more about "works on a planet where education is very rare".
The book includes complete blueprints for some very simple and not incredibly useful magic items, like a textbook on very basic electronics that will at least show you how to construct a crystal radio.