Abstract
This chapter builds upon the knowledge gained from previous chapters. It deals with more complex point groups and construction of character tables. The growth of group theory is remarkable and astonishing. It has developed into a powerful and influential area of study, not only for mathematicians but also with application to other major fields of sciences. Group theory extracts the crucial characteristics of diverse situations in which some type of transformation or symmetry appears. This chapter deals with representation of groups, reducible and irreducible representations, and character tables. Furthermore, it illustrates the application of quantum mechanics and molecular orbital correlation to group theory. Finally, the chapter introduces the way in which molecular spectroscopy involves a study of internal molecular motions such as vibrations and the importance of symmetry in these considerations.
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