An affine variety is a fundamental concept in algebraic geometry, representing a set of solutions to a system of polynomial equations. These solutions are considered within an affine space, which is a geometric structure that generalizes the properties of Euclidean space. Affine varieties can be defined over any field, such as the real numbers or complex numbers, and they can be finite-dimensional. Affine varieties can be classified as either irreducible or reducible. An irreducible affine variety cannot be expressed as the union of two smaller varieties, while a reducible variety can be broken down into simpler components. The study of affine varieties helps mathematicians understand the relationships between algebra and geometry.