Curve theory is a branch of mathematics that focuses on the study of curves in various geometrical contexts. This includes the study of the properties and characteristics of different types of curves, such as lines, circles, ellipses, and parabolas. Curve theory also involves the analysis of the behavior and relationships of curves in different spaces, such as Euclidean space, projective space, and differential geometry. Ultimately, curve theory aims to develop a deeper understanding of the geometric properties and structures of curves, leading to applications in various areas of mathematics and science.