This book presents a comprehensive theoretical basis of symmetry
representations of molecular vibrations, matrix representation of
symmetries, and the elements of group theory that are relevant to other
symmetry elements/operations, crystallographic and molecular point
groups. The book helps understand the reducible and irreducible
representations of symmetry matrices and then derive the normal modes of
vibration of different molecules by using suitable techniques
independently. Targeted to graduate students and researchers, this book
aims not only to derive the normal modes of vibration of any given
molecule themselves but also compares and verifies them with the
experimentally found modes by using IR and Raman-related techniques. For
the first time in the crystallographic history, this book presents the
group multiplication tables of all 32 point groups in both international
and Schoenflies notations.