  In this paper we develop the method of double operator integrals to prove
trace formulae for functions of contractions, dissipative operators, unitary
operators and self-adjoint operators. To establish the absolute continuity of
spectral shift, we use the Sz.-Nagy theorem on the absolute continuity of the
spectrum of the minimal unitary dilation of a completely nonunitary
contraction. We also give a construction of an intermediate contraction for a
pair of contractions with trace class difference.
