  We report a study of the distributions of the depth of maximum, Xmax, of
extensive air-shower profiles with energies above 10^17.8 eV as observed with
the fluorescence telescopes of the Pierre Auger Observatory. The analysis
method for selecting a data sample with minimal sampling bias is described in
detail as well as the experimental cross-checks and systematic uncertainties.
Furthermore, we discuss the detector acceptance and the resolution of the Xmax
measurement and provide parameterizations thereof as a function of energy. The
energy dependence of the mean and standard deviation of the Xmax-distributions
are compared to air-shower simulations for different nuclear primaries and
interpreted in terms of the mean and variance of the logarithmic mass
distribution at the top of the atmosphere.
