** Daqing Wan** (*UC Irvine*).

Given a polynomial f(x) over a finite field F_{q} of q elements,
we are interested in estimating the number of distinct values taken by
f(x) as x runs over the finite field F_{q}.
This problem has a long history,
and has received increasing attentions in recent years. In this lecture,
we try to give a comprehensive introduction to this topic and explain
the various points of view (analytic, algebraic/group theoretic,
geometric and algorithmic).