Historically, algebra grew out of the study of algebraic equations with numerical coefficients. Differential algebra sprang from the classical study of algebraic differential equations with coefficients that are meromorphic functions in a region of some complex m-dimensional space. This book provides a unified exposition of differential algebra in a purely algebraic setting. Topics included range from differential rings, fields, and polynomials to fields and their extensions, systems of equations, algebraic groups, and Galois theory.