Explore the mathematical theory of collapsing Calabi-Yau manifolds in this advanced mathematics lecture delivered by Valentino Tosatti at BIMSA's International Conference on Basic Sciences 2025. Delve into the complex geometric structures and analytical properties of these special manifolds as they undergo dimensional collapse, examining the limiting behavior and geometric transitions that occur in these fundamental objects of algebraic geometry and theoretical physics. Investigate the technical aspects of how Calabi-Yau manifolds behave under various collapsing scenarios, including the preservation of geometric properties, the formation of singularities, and the implications for string theory and mirror symmetry. Gain insights into current research developments in this specialized area of differential geometry, suitable for graduate students and researchers working in complex geometry, algebraic geometry, or mathematical physics.