  Braverman and Kappeler introduced a refinement of the Ray-Singer analytic
torsion associated to a flat vector bundle over a closed odd-dimensional
manifold. We study this notion and improve the Braverman-Kappeler theorem
comparing the refined analytic torsion with Farber-Turaev refinement of the
combinatorial torsion. Using this result we establish, modulo sign, the
Burghelea-Haller conjecture, comparing their complex analytic torsion with
Farber-Turaev torsion in the case, when the flat connection can be deformed in
the space of flat connections to a Hermitian connection. We also compute the
refined analytic torsion of lens spaces.
