Thaumium is a magical kind of ingot crafted from the crucible using eight Metallum and four Praecantatio. It is used to make a variety of thaumium weapons, as well as special kinds of magic blocks such as Arcane Stone Blocks.
Think of it as a base magic metal used to make other magic devices.
Before it can be crafted, the player must first research Basic Transmutation, and then Thaumium. (See research details)
Here's a video about Thaumium:
Thaumium is used in the crafting of the following items: