We give the classification of the maximal infinite algebraic subgroups of the real Cremona group of the plane up to conjugacy and present a parametrisation space of each conjugacy class. Moreover, we show that the real plane Cremona group is not generated by a countable union of its infinite algebraic subgroups.
"Infinite algebraic subgroups of the real Cremona group." Osaka J. Math. 55 (4) 681 - 712, October 2018.