This course provides the students with fundamental understanding of the symmetry elements, their operations, group theory and formation of character table as well as applications in spectroscopy. Topics to be discussed will include identification and classification of symmetry elements and operations, point group, Schönflies and Herman-Mauguin symmetry classification systems, high and low symmetry groups, reducible and irreducible representation, character table, ans orthogonality theorem as well as application of point group symmetry to IR and Raman activity, identification of polarity and chirality and symmetry adapted linear combination of atomic orbitals.