In this talk, we will explore the $L^{p}$-boundedness of both bilinear and multilinear maximal averages defined on non-degenerate hypersurfaces. Additionally, we will delve into the $L^2(\mathbb{R}^d)\times L^2(\mathbb{R}^d)\times\cdots\times L^2(\mathbb{R}^d) \to L^{2/m}(\mathbb{R}^d)$ estimates for $m$-linear maximal averages, focusing on hypersurfaces with $1\leq \kappa < md-1$ non-zero principal curvatures.

The video of this talk is available on the IISc Math Department channel.