The thaum is the basic unit of magic. Enthusiastic students together with Ponder Stibbons have found out that the thaum is made up of so called resons, which are themselves made up of at least five flavours (including up, down, sideways, sex appeal and peppermint). One thaum is defined to be the amount of magic which is needed to create a white pigeon or three billiard balls.
Another project related to the thaum is Ponder's Thaumic Reactor, designed deliberately to split the thaum and generate massive amounts of energy. As Ponder says, the energy that would be generated by such a thing would be enough to send the entire university to the moon. Or create a universe as the wizards did in 'The Science of Discworld '.