  In this article, we classify invariants and conjugacy classes of triangular
polynomial maps. We make these classifications in dimension 2 over domains
containing $\Q$, dimension 2 over fields of characteristic $p$, and dimension 3
over fields of characteristic zero. We discuss the generic characteristic 0
case. We determine the invariants and conjugacy classes of strictly triangular
maps of maximal order in all dimensions over fields of characteristic $p$. They
turn out to be equivalent to a map of the form $(x_1+f_1,\ldots,x_n+f_n)$ where
$f_i\in x_n^{p-1}k[x_{i+1}^p,\ldots,x_n^p]$ if $1\leq i\leq n-1$ and $f_n\in
k^*$.
