  Using the time-dependent Hartree-Fock-Bogoliubov approach, where the
condensate is coupled with the thermal cloud and the anomalous density, we
study the equilibrium and the dynamical properties of three-dimensional
quantum-degenerate Bose gas at finite temperature. Effects of the anomalous
correlations on the condensed fraction and the critical temperature are
discussed. In uniform Bose gas, useful expressions for the Bogoliubov
excitations spectrum, the first and second sound, the condensate depletion and
the superfluid fraction are derived. Our results are tested by comparing the
findings computed by Quantum Monte Carlo simulations. We present also a
systematic investigation of the collective modes of a Bose condensate confined
in an external trap. Our predictions are in qualitative agreement with previous
experimental and theoretical results. We show in particular that our theory is
capable of explaining the so-called anomalous behavior of the m=0 mode.
