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 truths, or theorems, within the system. The goal is to build a coherent and consistent body of knowledge based on these fundamental principles. In an axiomatic system, each theorem is logically deduced from the axioms and previously established theorems. This method ensures clarity and rigor, making it easier to understand complex concepts. Famous examples of axiomatic systems include Euclidean geometry and set theory, which have shaped much of modern mathematics.