Edoardo Lauria started his studies in Physics in Turin (Italy) and has concluded his Ph.D. at KU Leuven (Belgium) in 2018. His doctoral thesis has been published in the Springer Thesis series with the title “Points, Lines, and Surfaces at Criticality”. Currently, he holds a postdoctoral research position at Durham University and his research mainly focuses on conformal field theories.Antoine Van Proeyen is professor emeritus at KU Leuven, Belgium. He started his research on supergravity in 1979, soon after his Ph.D. He has been involved in the construction of various supergravity theories, resulting special geometries, relations to string theory and applications to phenomenology and cosmology. He is co-author of the textbook 'Supergravity' with prof. Dan Freedman and he published 150 research papers with an h impact factor over 50.

• 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.

Edoardo Lauria started his studies in Physics in Turin (Italy) and has concluded his Ph.D. at KU Leuven (Belgium) in 2018. His doctoral thesis has been published in the Springer Thesis series with the title “Points, Lines, and Surfaces at Criticality”. Currently, he holds a postdoctoral research position at Durham University and his research mainly focuses on conformal field theories.Antoine Van Proeyen is professor emeritus at KU Leuven, Belgium. He started his research on supergravity in 1979, soon after his Ph.D. He has been involved in the construction of various supergravity theories, resulting special geometries, relations to string theory and applications to phenomenology and cosmology. He is co-author of the textbook 'Supergravity' with prof. Dan Freedman and he published 150 research papers with an h impact factor over 50.

• 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.

Edoardo Lauria started his studies in Physics in Turin (Italy) and has concluded his Ph.D. at KU Leuven (Belgium) in 2018. His doctoral thesis has been published in the Springer Thesis series with the title “Points, Lines, and Surfaces at Criticality”. Currently, he holds a postdoctoral research position at Durham University and his research mainly focuses on conformal field theories.Antoine Van Proeyen is professor emeritus at KU Leuven, Belgium. He started his research on supergravity in 1979, soon after his Ph.D. He has been involved in the construction of various supergravity theories, resulting special geometries, relations to string theory and applications to phenomenology and cosmology. He is co-author of the textbook 'Supergravity' with prof. Dan Freedman and he published 150 research papers with an h impact factor over 50.

• 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.