Fixed-Point Theory is a branch of mathematics that studies points that remain unchanged under a given function. In simpler terms, if you apply a function to a specific point and the output is the same as the input, that point is called a fixed point. This concept is important in various fields, including computer science, economics, and dynamical systems. One of the key results in Fixed-Point Theory is the Brouwer Fixed-Point Theorem, which states that any continuous function mapping a compact convex set to itself has at least one fixed point. This theorem has numerous applications, such as in game theory and optimization problems, where finding stable solutions is essential.