This is the first of a series of papers devoted to the stabilization of the twisted trace formula. It is just an introduction. We present the local theory of twisted endoscopy, following the fundamental works of Kottwitz-Shelstad, Labesse and Shelstad. Our presentation is partly new because we try to give canonical definitions of the basic objects, which are more usually defined using auxiliary data. We prove also some results about the image of endoscopic transfer and about the dual transfer of stable distributions whose support is a finite set of stable conjugacy classes.
