The Renormalisation Group and the Renormalisation Group Equations

We describe the rigorous renormalisation group in the framework of the euclidean path integral, restricting (largely) to scalar fields. We start from a historical and conceptual overview leading from block spin transformations to the continuum description, with hindsight to critical phenomena. On the technical side we introduce some of the basic properties of Gaussian measures and perturbations thereof. The decomposition of the covariance of a Gaussian measure and its derivative with respect to a parameter lead to discrete (finite) or continuous (infinitesimal) renormalisation group transformations. The latter constitute the differential flow equations of renormalisation group. We comment on some generic results obtained with these methods. Finally we derive the Callan-Symanzik equations.