  These are short notes from a series of lectures given at the University of
Rennes in June 2013, at the University of Bonn in July 2013, at the XVIIth
Brazilian School of Probability in Mambucaba in August 2013, and at ETH Zurich
in September 2013. We give a concise overview of the theory of regularity
structures as exposed in Hairer (2014). In order to allow to focus on the
conceptual aspects of the theory, many proofs are omitted and statements are
simplified. We focus on applying the theory to the problem of giving a solution
theory to the stochastic quantisation equations for the Euclidean $\Phi^4_3$
quantum field theory.
