Convexity is a mathematical concept that pertains to the shape of a function or set. In simple terms, a function or set is considered convex if, for any two points within the function or set, the line segment connecting those two points lies entirely within the function or set. Convexity has many applications in various fields such as optimization, economics, engineering, and computer science. It allows for efficient solving of problems and provides insights into the structure of functions and sets. Convex optimization, in particular, is a key area of research that focuses on finding the optimal solutions of convex functions subject to constraints, with applications in machine learning, finance, and signal processing.