The fundamental concept of chemistry which refers to the symmetry present in the molecular structures and the classification of these molecules on the basis of their symmetry is called molecular symmetry. It attempts to explain the chemical properties of the molecules and their spectroscopic transitions. The basic framework for studying molecular symmetry is provided by the group theory. The subject of group theory can be classified into finite group theory, Lie theory and combinatorial and geometric group theory. Molecular symmetry classifies the different states of molecules by using the irreducible representations from the character table. X-ray crystallography and other forms of spectroscopy are used extensively for the assessment of molecular symmetry. Such selected concepts that redefine molecular symmetry and group theory have been presented in this book. Different approaches, evaluations and methodologies on molecular symmetry and group theory have been included herein. This book is a complete source of knowledge on the present status of this important field.