Theory of valuations on manifolds: a survey
  This is a non-technical survey of a recent theory of valuations on manifolds constructed in math.MG/0503397, math.MG/0503399, math.MG/0509512, math.MG/0511171 and actually a guide to this series of articles. We review also some recent related results obtained by a number of people. We formulate some open questions. 
Semyon Alesker