In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the real projective plane

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We study groups of biholomorphic and bimeromorphic automorphisms of projective hyperkähler manifolds. Using an action of these groups on some non-positively curved space, we immediately deduce many of their properties, including finite presentation, strong form of Tits' alternative, and some structural results about groups consisting of transformations with infinite order.

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting with invariant Picard number equal to one. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.Résumé. -On étudie les groupes d'automorphismes des surfaces de del Pezzo réelles, en se concentrant sur les groupes finis qui agissent avec un nombre invariant de Picard égal à 1. En conséquence, on obtient une bonne part de la classification des sous-groupes finis du groupe de Cremona du plan réel.