  The purpose of this article is to solve rough differential equations with the
theory of regularity structures. These new tools recently developed by Martin
Hairer for solving semi-linear partial differential stochastic equations were
inspired by the rough path theory. We take a pedagogical approach to facilitate
the understanding of this new theory. We recover results of the rough path
theory with the regularity structure framework. Hence, we show how to formulate
a fixed point problem in the abstract space of modelled distributions to solve
the rough differential equations. We also give a proof of the existence of a
rough path lift with the theory of regularity structure.
