  These are lecture notes from a course in arithmetic dynamics given in
Grenoble in June 2017. The main purpose of this text is to explain how
arithmetic equidistribution theory can be used in the dynamics of rational maps
on P^1. We first briefly introduce the basics of the iteration theory of
rational maps on the projective line over C, as well as some elements of
iteration theory over an arbitrary complete valued field and the construction
of dynamically defined height functions for rational functions defined over
\overline Q. The equidistribution of small points gives some original
information on the distribution of preperiodic orbits, leading to some
non-trivial rigidity statements. We then explain some consequences of
arithmetic equidistribution to the study of the geometry of parameter spaces of
such dynamical systems, notably pertaining to the distribution of special
parameters and the classification of special subvarieties.
