Kantorovich metric:initial history and little-known applications

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.