Dixmier traces and some applications to noncommutative geometry
  This is a survey of some recent advances in the theory of singular traces in which the authors have played some part and which were inspired by questions raised by the book of Alain Connes (Noncommutative Geometry, Academic Press 1994). There are some original proofs and ideas but most of the results have appeared elsewhere. Detailed information on the contents is contained in the Introduction. 
A.L. Carey, F. A. Sukochev