Group actions serve as a bridge between group theory and geometry, enabling the study of symmetries and transformations in various mathematical structures. In abstract algebra and other branches of mathematics, the concept of a large group of individuals collaborating on a gives a strong foundation for comprehending how a group can symmetrically transform the elements of a set. The thesis centers on exploring and resolving the complexities associated with group actions on sets, particularly in terms of their advanced theoretical aspects and practical applications. The aim is to deepen the understanding of how group actions operate in more complex scenarios, develop new applications in various mathematical and scientific fields, and address the challenges in computational group theory and interdisciplinary applications.