A Hilbert System is a type of formal proof system used in mathematical logic and proof theory. It consists of a set of axioms and inference rules that allow for the derivation of theorems. The system is named after the mathematician David Hilbert, who contributed significantly to the foundations of mathematics. In a Hilbert System, proofs are typically structured as sequences of statements, where each statement is either an axiom, an assumption, or derived from previous statements using the inference rules. This approach emphasizes the formal structure of logical reasoning, making it easier to analyze the validity of arguments within a given logical framework.