In this chapter, we introduce some basic formalism of differential algebra. This may viewed as a mild perturbation of commutative algebra, in which we consider commutative rings equipped with the additional noncommutative structure of a derivation. This allows us to manipulate differential equations and differential systems in a manner that keeps a bit more useful structure visible, though we will need to convert back and forth from this point of view. A particularly important result we introduce is the cyclic vector theorem, which gives a compact but highly noncanonical way to represent a finite differential module over a field. While the cyclic vector theorem will prove indispensable at a few key points in our treatment of p-adic differential equations, we will ultimately make more progress by limiting its use.