**Hagen Triendl**

*Extended and Gauged Supergravity*

We will discuss supergravity theories with extended supersymmetry (N=2, 4 and 8) and gaugings thereof. In particular the geometry of the scalar manifold and the gauge-kinetic function will be characterized, and the couplings and the scalar potential induced by gaugings are introduced. Subsequently we discuss the occurence of these supergravities in string compactifications and important applications such as spontaneous supersymmetry breaking and supersymmetric black holes.

**Leonardo Castellani**

* Supergravity I*

In my lectures I will cover:

- N=1 D=4 supergravity in components.
- Group-geometric approach, superfields and superspace.
- Auxiliary fields and off-shell closure of the supersymmetry algebra
- Superalgebras, spinors in higher dimensions.
- Supergravities in higher dimensions, Kaluza-Klein compactifications.

**Branislav Cvetkovic**

*Poincaré gauge theory*

Throughout the course we review the basic structure of Poincaré gauge theory (PGT) of gravity, with emphasis on its fundamental principles and geometric interpretation as well as possible applications. This 5 days course includes the following topics:

- Global Poincaré symmetry, the symmetry of the fundametal interactions in the absence of gravity.
- Localization of Poincaré symmetry, introduction of compensating fields which are found to represent gravitational interaction.
- Geometric interpretation of PGT and the underlying Riemann-Cartan structure of spacetime.
- Einstein-Cartan theory as the simplest example of PGT and its applications in cosmology.

**Voja Radovanovic**

*Introduction to Supersymmetry*

In theses lectures we give a brief introduction to N=1 D=4 supersymmetry. We will discuss: Lorentz and Poincare group, two component (Weyl) spinors, Fierz identites, super-Poincare algebra. Using the formalism of superfields we will construct the Wess-Zumino model and

super-Yang-Mills theories.