  Todays key information on the shape of the unitarity triangle is obtained
from the well-measured quantity epsilon_K characterizing the CP-violation in
|Delta S|=2 transitions. The phenomenological analysis requires the input of
four key quantities: The magnitudes of the CKM elements V_cb and V_ub, the top
quark mass and the non-perturbative parameter B_K. In the recent years all of
them have been determined with increasing precision. In order to keep up with
this progress the |Delta S|=2-hamiltonian had to be obtained in the
next-to-leading order (NLO) of renormalization group improved perturbation
theory. I present the NLO results for the QCD coefficients eta_1 and eta_3,
which have been calculated by Stefan Herrlich and myself, and briefly sketch
some aspects of the calculation. Then I give an update of the Unitarity
Triangle using the summer 1996 data for the input parameters. The results for
the improved Wolfenstein parameters rho-bar and eta-bar and the CKM phase delta
are -0.21 < rho-bar < 0.22, 0.27 < eta-bar < 0.43 and 57 degrees < delta < 122
degrees. The range for the quantity sin(2 beta) entering CP asymmetries in
B-decays is found as 0.46 < sin(2 beta) < 0.79. The given ranges correspond to
one standard deviation in the input parameters. Finally I briefly discuss the
K_L-K_S mass difference.
