Inverse Problems : Lectures given at the 1st 1986 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Montecatini Terme Italy May 28 – June 5 1986 Inverse eigenvalue problems Regularization methods for linear inverse problems Some mathematical problems motivated by medical imaging Numerical treatment of ill posed problems Regularization with linear equality constraints On the inversion of some first kind fredholm equations occurring in optical applications.