The course aims to give an overview of modern developments in statistical mechanics. In particular, starting from the theory of phase transitions and critical phenomena, we want to show how the concepts underlying the method of the re-normalization group emerged. This method is now widely used in various fields of statistical mechanics. The critical phenomena constitute the classical application of the method, which is illustrated in detail in the first 6 credits of the course. These first 6 credits can therefore be used by multiple addresses. The remaining 2 credits focus on more recent applications of the method in the field of matter physics.