A Polynomial Ring is a mathematical structure formed by polynomials, which are expressions made up of variables and coefficients. In a polynomial ring, you can add, subtract, and multiply polynomials, following specific rules. The most common example is the ring of polynomials in one variable, denoted as R[x], where R represents a set of coefficients, such as real numbers or integers. Polynomial rings can also be extended to multiple variables, like R[x, y], allowing for more complex expressions. These rings are essential in various fields of mathematics, including algebra and calculus, and are used to solve equations and model real-world phenomena.