  There are many equivalent ways to describe the p-torsion of a principally
polarized abelian variety in characteristic p. We briefly explain these methods
and then illustrate them for abelian varieties A of arbitrary dimension g in
several important cases, including when A has p-rank f and a-number 1 and when
A has p-rank f and a-number g-f. We provide complete tables for abelian
varieties of dimension up to four.
