Hilbert Theory is a branch of mathematics that focuses on the study of algebraic equations and their solutions. Named after the mathematician David Hilbert, it explores the relationships between different types of algebraic structures, such as fields and rings. The theory provides a framework for understanding how these structures can be manipulated and solved. One of the key aspects of Hilbert Theory is the concept of Hilbert spaces, which are infinite-dimensional spaces used in various areas of mathematics and physics. These spaces allow for the generalization of geometric concepts and are essential in the study of functional analysis and quantum mechanics.