Introduction Basic Ingredients Gauging spacetime symmetries and the Weyl multiplet Matter Multiplets Gauge fixing of superconformal symmetries Special Kähler geometry Action and main transformation laws from general considerations Quaternionic and very special geometry Final results Further developments Appendices.

This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions. First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized. Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kähler manifolds. This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.

Introduction Basic Ingredients Gauging spacetime symmetries and the Weyl multiplet Matter Multiplets Gauge fixing of superconformal symmetries Special Kähler geometry Action and main transformation laws from general considerations Quaternionic and very special geometry Final results Further developments Appendices