An algebraic set is a collection of points in a space that satisfy a given set of polynomial equations. These points can be represented in various dimensions, such as in two-dimensional or three-dimensional space. Algebraic sets are fundamental in algebraic geometry, where they help in understanding the geometric properties of solutions to polynomial equations. In the context of affine space, an algebraic set can be defined as the set of all points whose coordinates satisfy specific polynomial equations. For example, the equation x^2 + y^2 = 1 describes a circle, which is an algebraic set in the plane. Algebraic sets can also be studied in projective space, where they take on different forms and properties.