An axiomatic system is a structured framework in mathematics and logic that begins with a set of basic assumptions, known as axioms. These axioms are accepted as true without proof and serve as the foundation for deriving further statements, called theorems. The goal is to build a coherent system where all conclusions logically follow from the initial axioms. In an axiomatic system, the relationships between axioms and theorems are defined through rules of inference. This approach is fundamental in various fields, including geometry, set theory, and formal logic, allowing for rigorous proofs and a clear understanding of mathematical concepts.