Functional Analysis is a branch of mathematics that focuses on the study of vector spaces and the functions that act on them. It explores how these functions behave and interact, particularly in infinite-dimensional spaces. This area of study is essential for understanding various concepts in calculus, differential equations, and quantum mechanics. One of the key ideas in Functional Analysis is the concept of normed spaces, which measure the size of vectors and functions. By analyzing these spaces, mathematicians can solve complex problems and develop theories that apply to real-world situations, such as in engineering and physics.