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These are short 2014 lecture notes by M. Hairer giving 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. The focus is 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.
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