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The success of the first edition of this book has encouraged us to revise and update it. In the second edition we have attempted to further clarify por- tions of the text in reference to point symmetry, keeping certain sections and removing others. The ever-expanding interest in solids necessitates some discussion on space symmetry. In this edition we have expanded the discus- sion on point symmetry to include space symmetry. The selection rules in- clude space group selection rules (for k = 0). Numerous examples are pro- vided to acquaint the reader with the procedure necessary to accomplish this. Recent examples from the literature are given to illustrate the use of group theory in the interpretation of molecular spectra and in the determination of molecular structure. The text is intended for scientists and students with only a limited theoretical background in spectroscopy. For this reason we have presented detailed procedures for carrying out the selection rules and normal coor- dinate treatment of molecules. We have chosen to exclude discussion on symmetry aspects of molecular orbital theory and ligand field theory. It has been our approach to highlight vibrational data only, primarily to keep the size and cost of the book to a reasonable limit.