Convex Analysis is a branch of mathematics that studies the properties and applications of convex sets and convex functions. A set is convex if, for any two points within it, the line segment connecting those points lies entirely within the set. Similarly, a function is convex if its graph lies below the line segment connecting any two points on the graph. This field has important implications in various areas, including optimization, economics, and game theory. Techniques from Convex Analysis help in solving problems where finding the best solution is crucial, such as minimizing costs or maximizing profits in economics.