Explore algebraic actions on complex varieties and their real forms in this lecture from the Brazil-France School on Foliation Theory. Delve into advanced mathematical concepts as part of a collaborative event hosted simultaneously at CIRM in Marseille and IMPA in Rio de Janeiro. Learn from expert mathematicians in the field of foliation theory through a series of mini-courses and short talks designed to foster international collaboration and knowledge exchange between Brazilian and French mathematical communities. Gain insights into cutting-edge research and developments in this specialized area of mathematics, suitable for graduate students, post-doctoral researchers, and established mathematicians interested in expanding their understanding of complex algebraic geometry and foliation theory.