The Hilbert System is a formal system in mathematical logic and proof theory, named after the mathematician David Hilbert. It is designed to provide a framework for deriving theorems using a set of axioms and inference rules. The system emphasizes the use of a finite number of axioms and rules to construct proofs, making it a foundational approach in formal logic. In a Hilbert System, each statement can be derived from axioms through a series of logical deductions. This method is particularly significant in the study of first-order logic and has influenced various areas of mathematics and computer science, including automated theorem proving.