The group theory was developed in the nineteenth century to solve equations. The groups play an important role in developing various applications in Mathematics, computer sciences, cryptography, medical sciences, biology, and many other related fields. For a better understanding of the groups, an imagination of the learners must be righteous. This chapter deals with the various operations, groups, subgroups, cyclic group, normal subgroup, homomorphism, isomorphism, and group codes with precise examples. The chapter defines the concepts of group and related theories by using the experiment of the common family BHAAHA having three members. It explains how group theory connects with regular family activities. Moreover, due to the various applications in Artificial Intelligence and Machine Learning, group theory is in the limelight of scientists of various fields. The chapter culminates in case studies, projects and pedagogical exercises aimed at reconciling theoretical relational frameworks with their multidisciplinary applications.