In this lecture, I will review the Grothendieck-Lefschetz trace formula, which gives a formula for counting the number of points of an algebraic variety in terms of the etale cohomology of that variety. I'll then explain how it can be combined with the nonabelian Poincare duality of the preceding lectures to count principal G-bundles on algebraic curves, leading to a proof of Weil's conjecture in the function field case.