THE COMPLETE FORM OF N=2 SUPERGRAVITY AND ITS PLACE IN THE GENERAL FRAMEWORK OF D=4 N-EXTENDED SUPERGRAVITES

Relying on the geometrical set up of Special Kahler Geometry and Quate rnionic Geometry, which I discussed at length in my Lectures at the 19 95 edition of this Spring School, I present here the recently obtained fully general form of N=2 supergravity with completely arbitrary coup lings. This lagrangian has already been used in the literature to obta in various results: notably the partial breaking of supersymmetry and various extremal black-hole solutions. My emphasis, however, is only o n providing the reader with a completely explicit and ready to use com ponent expression of the supergravity action. All the details of the d erivation are omitted but all the definitions of the items entering th e lagrangian and the supersymmetry transformation rules are given.