  This is a note of talks I gave at the number theory seminar at Tsinghua
University in Fall 2011.
  We will introduce the local and global Euler characteristic formulas given by
John Tate(1962) for Galois cohomology. We will give a detailed proof based on
the idea in Hida's book[1,ch4.4.5] and Milne's book[2,ch1.5].
