The concept of groups had its origin more than 150 years ago, in the beginning of the nineteenth century. The early development of the “Group Theory” was due to famous mathematicians Gauss, Cauchy, Abel, Hamilton, Cayley and many others. However, till the advent of the modern quantum mechanics in 1925, it did not find much use in physics. The advantages of group theory in physics were soon recognized and the new tool was put to use in the calculations of the atomic structures and spectra by H.A. Bethe, E.P. Wigner and many others. Group theory has now become indispensable in the most branches of physics and physical chemistry. Group theory plays a major role in the solution of solid state physics problems. The concept of symmetry plays an important role in our physical environment. The symmetry of a molecule can be used to determine the various physical properties of a crystal using group theoretical methods.