In the present subject Quantum Mechanics is applied to the study of molecules and the fundamentals of molecular spectroscopy. First, the Born-Oppenheimer approximation is introduced and the concept of potential energy surface presented, so a relatively detailed study of the rotation and vibration-rotation spectroscopies can later be done. The molecular orbital (MO) and valence bond (VB) methods for the analysis of the electronic structure of molecules are presented, so that of simple molecules can be studied and some basic aspects discussed. The concepts needed for studying the electron and photoelectron spectroscopies are, therefore, given. The most important computational methods for the study of the electronic structure, which form the basis of Computational Chemistry, are also presented in a simple way. The analysis of the spectroscopic methods includes the fundamentals of the magnetic resonance techniques, which is done from a theoretical perspective, as well as those of some other methods, including those based on the use of the laser. The theoretical developments studied in this subject rely on the fundamentals of Quantum Mechanics and the models for translation, vibration and rotation as presented in Química Física III: Química Cuántica. The introduction to Group Theory provided in that subject is completed in the present one by the first theme. Some elements of Statistical Mechanics are used to analyze the intensity and width/shape of the spectral lines for instance. By its theoretical and experimental contents, it provides some support to Química Física V: Cinética Química.