Explore the cutting edge of foliation theory with “Extrinsic Geometry of Foliations.” This pivotal work delves into geometric problems within this modern branch of Riemannian Geometry, focusing on the concept of mixed curvature. Discover a comprehensive examination of Ricci curvature for mixed curvature of foliations. Across five chapters, delve into integral and variation formulas, curvature, and the dynamics of foliations. The book showcases diverse approaches—local and global, regular and singular—employing integral formulas, extrinsic geometric flows, generalized curvatures, pseudo-Riemannian geometries, and Finsler metrics. A valuable resource for researchers and graduate students in Riemannian geometry, foliation theory, and differential topology, this volume represents the authors’ extensive work and offers insights into the state-of-the-art geometric and analytical theories.