This survey explores mutation testing, a technique widely used to assess software testing quality. It covers the formal definition, steps for generating and executing mutants, different mutation classes, types, and industrial applications. Mutation testing plays a crucial role in identifying weaknesses in test suites and improving overall fault-detection capability. The survey emphasizes the significance of mutation testing in software development and offers valuable insights to researchers and practitioners. It discusses theoretical foundations, including mutation operators and equivalent mutants, and practical aspects such as generating and executing mutants. Various mutation types are categorized based on their characteristics and scope. Real-world applications in industry highlight its effectiveness in enhancing software quality. This survey serves as a comprehensive resource for understanding mutation testing and provides directions for future research and development.