Differential algebra is a branch of mathematics that studies algebraic structures equipped with a differentiation operation. It combines concepts from both algebra and calculus, allowing for the analysis of functions and their derivatives in a formal way. This field is particularly useful in understanding systems of differential equations and their solutions. In differential algebra, one often works with differential fields, which are fields that include a derivation—a function that mimics the properties of differentiation. This approach can be applied to various areas, including control theory, dynamical systems, and algebraic geometry, providing a framework for solving complex problems involving rates of change.