This atlas is the first one in the field of vibrational spectroscopy of polyatomic molecules. It is divided into two paragraphs. The first deals with the theory of vibrational spectroscopy in a concise form and considers the most important spectroscopical parameters - frequencies, bandshape and intensities. The second paragraph is dedicated to the infrared (2000-400 cm-1), far infrared (400-40 cm-1) and Raman (2000-10 cm-1) spectra of about hundred different mesomorphic materials with various molecular structure. The polarized IR spectra of the most important liquid crystals is also included. In the second paragraph the assignment of the IR bands to the corresponding intramolecular vibrations is also reported. Almost all spectra is registrated and analysed for the first time. The major important features are: 1. Registration and analysis (for the first time) of vibrational spectra of polyatomic molecules with mesomorphic phases; 2. Registration (for the first time) of vibrational spectra of polyatomic molecules with mesomorphic phase in polarized IR light. Polarized vibrational spectra are very important for clarification of the molecular structure; 3. Assignment (for the first time) of the IR bands of the most important liquid crystalline materials to the corresponding vibrations.