For the Sixth Course of the International School of Cosmology and Gravitation of the "Ettore Maj orana" Centre for Scientific Cul ture we choose as the principal topics torsion and supergravity, because in our opinion it is one of the principal tasks of today's theoretical physics to attempt to link together the theory of ele mentary particles and general relativity. Our aim was to delineate the present status of the principal efforts directed toward this end, and to explore possible directions of work in the near future. Efforts to incorporate spin as a dynamic variable into the foundations of the theory of gravitation were poineered by E. Cartan, whose contributions to this problem go back half a century. Accord ing to A. Trautman this so-called Einstein-Cartan theory is the sim plest and most natural modification of Einstein's 1916 theory. F. Hehl has contributed a very detailed and comprehensive analysis of this topic, original view of non-Riemannian space-time. Characteristic of Einstein-Cartan theories is the enrichment of Riemannian geometry by torsion, the non-symmetric part of the otherwise metric-compatible affine connection. Torsion has a impact on the theory of elementary particles. According to V. de Sabbata, weak interactions can be based on the Einstein-Cartan geometry, in that the Lagrangian describing weak interactions and torsion inter- action possess analogous structures, leading to a unification of weak and gravitational forces.

Contenu
I: Theories with Torsion.- Generalities on Geometric Theories of Gravitation.- Four Lectures on Poincaré Gauge Field Theory.- The Macroscopic Limit of the Poincaré Gauge Field Theory of Gravitation.- QuasiClassical Limit of the Dirac Equation and the Equivalence Principle in the Riemann-Cartan Geometry.- Contracted Bianchi Identities and Conservation Laws in Poincaré Gauge Theories of Gravity.- The Gauge Symmetries of Gravitation.- The Motion of Test-Particles in Non-Riemannian Space-Time.- Torsion and Strong Gravity in The Realm of Elementary Particles and Cosmological Physics.- III: Supersymmetries, Twistors and Other Symmetry Groups.- The Fading World Point.- Superalgebras, Supergroups, and Geometric Gauging.- Four Lectures at the 1979 Erice School on Spin, Torsion, Rotation, and Supergravity.- Self Dual Fields.- An Introduction to Complex Manifolds.- A Brief Outline of Twistor Theory.- III: Experimental Relativity and Other Topics.- Experimental Gravitation with Measurements Made from Within a Planetary System.- Tests of General Relativity at the Quantum Level.- The Mass-Angular Momentum-Diagram of Astronomical Objects.- Bimetric General Relativity Theory.- Covariance and Quantum Physics-Need for a New Foundation of Quantum Theory?.- Relativistic Equations of Motion of Spin Particles.- Angular Momentum of Isolated Systems in General Relativity.- Isometries and General Solutions of Non-Linear Equations.- On the Visual Geometry of Spinors and Twistors.- Gravitation Photoproduction in Static Electromagnetic Fields and Some Astrophysical Applications.- Invariant Deduction of the Gravitational Equations from the Principle of Hamilton.- On a Generalization of the Notion of Reimann Curvature and Spaces with Torsion.- Comments on the Paper by Elie Cartan: Sur une Generalisation de la Notion de Courbure de Riemann et les Espaces a Torsion.