Non-commutative spaces in physics and mathematics
  The present review aims both to offer some motivations and mathematical prerequisites for a study of NCG from the viewpoint of a theoretical physicist and to show a few applications to matrix theory and results obtained.   Lectures given by the author at the TMR School on contemporary string theory and brane physics, 26 Jan--2 Feb 2000, Torino. 
Daniela Bigatti (K.U. Leuven)