Kähler geometry is a branch of differential geometry that studies a special type of manifold called a Kähler manifold. These manifolds have a rich structure, combining both symplectic and complex geometries. A Kähler manifold is equipped with a Riemannian metric that is compatible with a complex structure, allowing for the definition of a Kähler metric. The significance of Kähler geometry lies in its applications in various fields, including string theory, algebraic geometry, and mathematical physics. Kähler manifolds often exhibit nice properties, such as being Ricci-flat or having a well-defined notion of curvature, making them important in both theoretical and applied contexts.