Convex geometry is a branch of mathematics that studies convex sets and their properties. A set is considered convex if, for any two points within the set, the line segment connecting them also lies entirely within the set. This concept is fundamental in various fields, including optimization, computer graphics, and economics. Key topics in convex geometry include convex hulls, which are the smallest convex sets containing a given set of points, and convex functions, which have specific properties that make them useful in optimization problems. The study of convex shapes helps in understanding geometric structures and their applications in real-world scenarios.