Operator theory is a branch of functional analysis that focuses on studying linear operators on vector spaces, particularly in the context of infinite-dimensional spaces. This field deals with properties and behavior of operators, such as boundedness, invertibility, spectrum, and convergence. Operator theory has applications in various areas of mathematics, physics, and engineering, including quantum mechanics, signal processing, and control theory. It plays a crucial role in understanding the behavior of linear systems and functions in complex mathematical structures.