An affine space is a geometric structure that generalizes the properties of Euclidean space, such as points, lines, and planes, to include translations and parallelism. In an affine space, there is no fixed origin or coordinate system, but instead, all points are defined relative to each other. Affine spaces are characterized by their linear structure, which allows for the study of transformations such as translations, rotations, and reflections. Unlike Euclidean spaces, affine spaces do not have a notion of distance or angle, but they do have a concept of parallelism. Affine spaces have applications in many areas of science and engineering, including physics, computer graphics, and optimization theory.