  In these notes, we provide an introduction to a new regularity structure used
for solving rough mean-field equations.
  The index set of this regularity structure is described a collection of novel
objects which we refer to as Lions trees. These objects arise in Taylor
expansions involving the Lions derivative and capture many of the desirable
properties of mean-field dynamics.
  This work represents a comprehensive generalisation of the ideas first
introduced in [BCD20] that promise powerful insights into how interactions with
a collective determine the dynamics of an individual within this collective.
