Conservation theorems are central to many aspects of physics: they often form the central reasoning principles for new observations, they provide checks on new predictions, and they appear to be obeyed regardless of system and scale. You might not have heard them called conservation theorems before, but you have used them. In mechanics, these theorems manifest themselves as the three fundamental principles (for momentum, energy, and angular momentum):

$$\Delta \vec{p}_{sys} = \vec{F}_{ext} \Delta t$$ $$\Delta {E}_{sys} = W_{ext} + Q$$ $$\Delta \vec{L}_{sys} = \vec{\tau}_{ext} \Delta t.$$

Electromagnetism is consistent with these fundamental principles (as you will see), but now that matter has charge, we bring a fourth fundamental principle to the party,

$$\Delta Q_{sys} = I_{ext} \Delta t.$$

These principles are referred to as “conservation theorems” because the describe how properties of a system will change and, in principles, under what conditions those properties will not change (i.e., how they are conserved),

$$\Delta \vec{p}_{sys} = 0\,\mathrm{when}\, \vec{F}_{ext} = 0$$ $$\Delta {E}_{sys} = 0\,\mathrm{when}\, W_{ext} + Q = 0$$ $$\Delta \vec{L}_{sys} = 0\,\mathrm{when}\, \vec{\tau}_{ext} = 0$$ $$\Delta Q_{sys} = 0\,\mathrm{when}\, I_{ext} = 0$$