  We discuss the mean values of multiplicative functions over function fields.
In particular, we adapt the authors' new proof of Halasz's theorem on mean
values to this simpler setting. Several of the technical difficulties that
arise over the integers disappear in the function field setting, which helps
bring out more clearly the main ideas of the proofs over number fields. We also
obtain Lipschitz estimates showing the slow variation of mean values of
multiplicative functions over function fields, which display some features that
are not present in the integer situation.
