Real Methods in Complex and CR Geometry : Lectures given at the C.I.M.E. Summer School held in Martina Franca Italy June 30 July 6 2002 The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.s boundary value problems induced equations analytic discs in symplectic spaces complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity