A Fano manifold is a special type of complex manifold that has positive first Chern class. This property implies that Fano manifolds have ample line bundles, which means they can support a rich structure of holomorphic sections. They are important in algebraic geometry and play a crucial role in the study of Kähler manifolds. Fano manifolds are often studied for their geometric properties and their connections to mirror symmetry and string theory. Examples include projective spaces and certain varieties like Cubic hypersurfaces. Their unique characteristics make them a central topic in modern mathematics.