Exponential sums and l-adic cohomology:: A survey

This is the text of two lectures given at the Exponential Sums Conference held at The Hebrew University of Jerusalem in January 1998. In these lectures I reviewed some important results on exponential sums, which have been obtained by Deligne, Katz and others as consequences of the Grothendieck trace formula for the e-adic cohomology and Deligne's fundamental result on the Well conjecture.