  In this paper geometry of Gromov-Hausdorff distance on the class of all
metric spaces considered up to an isometry is investigated. For this class
continuous curves and their lengths are defined, and it is shown that the
Gromov-Hausdorff distance is intrinsic. Besides, metric segments are
considered, i.e., the classes of points lying between two given ones, and an
extension problem of such segments beyond their end-points is considered.
