These notes are based on a series of talks given by V. Voevodsky
at the AMS Summer Research Conference on algebraic K-theory,
held in Seattle during July 1997.
The purpose of Voevodsky's talks, reflected in these notes, was to
outline his proof of ``Milnor's conjecture'' that the Milnor K-theory
of a field F, reduced modulo two, is isomorphic to the etale cohomology
of F with coefficients Z/2.
This paper appeared in Proc. Symp. Pure Math. 67 (1999), 283-304.