  In this note, we present the theorem of extension of birational group laws in
both settings of classical varieties (Weil) and schemes (Artin). We improve
slightly the original proof with a more direct construction of the group
extension and the systematic use of algebraic spaces, and we discuss the
separation properties of the group extension. We also explain the important
application to the construction of N\'eron models of abelian varieties. This
note grew out of lectures given by Ariane M\'ezard and the second author at the
Summer School "Sch\'emas en groupes" held in the CIRM (Luminy) from 29 August
to 9 September, 2011.
