  The short history of L.Kantorovich's transport problem and his metric in the
framework of his activity in mathmatics and economics during a long and
difficult period. We did not mention the recent impetuious developement of
application of the transport probelm to differential equations etc., and
concentrated on three applications not known to wide audience - in measure and
ergodic theory, and metric geometry and classification of mertric spaces with
measures.
  This is a detale version of the talk of author on the Conference devoted to
  90-th annyversary of Leonid.V.Kantorovich which was at St.Petersbutrg Euler
International Mathematical Institute in January 2004.
