In this books, we provide fundamental definitions of key algebraic concepts that are essential for our study. Additionally, we present a brief overview of the contributions made by several researchers in this field, including E.C. Posnar, M. Bresar, J. Vukman, H.E. Bell, M.N. Daif, W.S. Martindale, B. Hvala, I.N. Herstein, M. Asharf, Shakir Ali, J.H. Mayne, N. Argac, Ajda Fosner, N. Nobusawa, Gy. Maksa, M. Samman, N. Alyamani, and M.J. Atteya, B. Zalar.