Statistical mechanics is a branch of physics aiming at understanding the laws of the macroscopic behaviour of systems composed of many microscopic components. Critical phenomena, such as phase transitions, involve a drastic change in the macroscopic state by tuning model parameters. Critical phenomena are extremely universal far beyond physics, for instance in chemistry, biology or complex systems. In this course, we aim to give a mathematical foundation for the study of many component systems on the lattice and in the continuum space. Moreover, we would like to motivate the theory of Gibbs measures starting from basic principles in classical mechanics.