Explore the intricacies of local invariant hypersurfaces for codimension one foliation in this 35-minute conference talk presented at the Brazil-France School on Foliation Theory. Delve into advanced mathematical concepts as part of a collaborative event hosted simultaneously at the Centre International de Rencontres Mathématiques (CIRM) in Marseille and the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. Gain insights from this specialized lecture, which is one component of a broader school featuring four mini-courses and additional short talks by PhD students and young post-docs. Benefit from the long-standing collaboration between Brazilian and French communities in foliation theory, and engage with cutting-edge research in this field of mathematics.